A Level Physics (A2) formulas

Every chapter of A Level Physics (A2) on one page: the 296 formulas, definitions and facts to remember, in syllabus order. Use it for a last look before a test, then check yourself.

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Motion in a circle

Kinematics of uniform circular motion

angle in radians = arc length ÷ radius (θ = s/r)
360° = 2π rad, so 1 rad ≈ 57.3°; to change degrees to radians multiply by π/180
angular speed = angle turned ÷ time taken (ω = θ/t), unit rad s⁻¹
angular speed = 2π ÷ period (ω = 2π/T); also ω = 2πf, where f is the number of revolutions per second
linear speed = radius × angular speed (v = rω)
Points on the same rotating body: same ω, but v is proportional to r

Centripetal acceleration

centripetal acceleration = radius × (angular speed)² (a = rω²)
centripetal acceleration = (speed)² ÷ radius (a = v²/r)
centripetal force = mass × centripetal acceleration (F = mrω² = mv²/r)
Acceleration and resultant force both point towards the centre, at 90° to the velocity
Constant in uniform circular motion: speed, angular speed, kinetic energy and the magnitudes of a and F. Not constant: velocity, momentum and the directions of a and F
Vertical circle, lowest point: tension − weight = mv²/r

Gravitational fields

Gravitational field

gravitational field strength = force ÷ mass (g = F/m), unit N kg⁻¹
force on a mass in a field = mass × field strength (F = mg); this force is the weight
Field lines point towards the mass that causes the field and never cross
Closer lines mean a stronger field; equally spaced parallel lines mean a uniform field
Radial field: around a point mass or outside a uniform sphere; g gets smaller with distance
g is a vector, so the fields of two masses add as vectors; between two masses they are in opposite directions

Gravitational force between point masses

gravitational force = G × mass 1 × mass 2 ÷ (separation)² (F = Gm₁m₂/r²), with G = 6.67 × 10⁻¹¹ N m² kg⁻²
r is the distance between centres: for a satellite at height h, r = R + h
Circular orbit: GMm/r² = mv²/r, so v = √(GM/r)
Period: T² = 4π²r³/(GM), so T² is proportional to r³
A larger orbit means a lower speed and a longer period
Geostationary orbit: period 24 hours, west to east, above the Equator

Gravitational field of a point mass

gravitational field strength = G × mass ÷ (distance from centre)² (g = GM/r²)
Derivation: F = GMm/r² and g = F/m, so g = GM/r²
g is proportional to 1/r²: 2r gives g/4, 3r gives g/9
At the surface r = R; at height h, r = R + h
For comparing planets: g is proportional to M/R²
Small heights (h much less than R): g is approximately constant, about 9.81 N kg⁻¹ at the Earth

Gravitational potential

gravitational potential = −G × mass ÷ distance from centre (ϕ = −GM/r), unit J kg⁻¹
ϕ = 0 at infinity and is negative everywhere else
potential energy = mass × potential (E_P = mϕ)
For two point masses: E_P = −GMm/r
work done = mass × change in potential (W = mΔϕ)
Moving from r₁ out to r₂: increase in E_P = GMm(1/r₁ − 1/r₂)
ϕ is proportional to 1/r, but g is proportional to 1/r²

Temperature

Thermal equilibrium

Net thermal energy transfer is from higher temperature to lower temperature
Thermal equilibrium: same temperature, so no net transfer of thermal energy
Objects in thermal equilibrium need not have the same internal energy, mass or heat capacity
If A is in equilibrium with B, and B with C, then A is in equilibrium with C
Mixing with no losses: energy lost by the hot object = energy gained by the cold object
A thermometer reads its own temperature, so it must first reach equilibrium with the object

Temperature scales

temperature in kelvin = temperature in °C + 273.15 (T/K = θ/°C + 273.15); 273 is usually accurate enough
Absolute zero = 0 K = −273.15 °C, the lowest possible temperature
A change of 1 K is the same size as a change of 1 °C
Thermometric properties: density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple
Linear scale: θ = 100 × (X − X₀)/(X₁₀₀ − X₀) °C, where X is the value of the property
The thermodynamic scale does not depend on the property of any substance

Specific heat capacity and specific latent heat

energy = mass × specific heat capacity × temperature change (E = mcΔθ)
Unit of c: J kg⁻¹ K⁻¹
energy = mass × specific latent heat (E = mL)
Unit of L: J kg⁻¹
Electrical heating: energy supplied = power × time (E = Pt)
Steady flow or steady boiling: power = (mass per second) × cΔθ, or (mass per second) × L
Two readings with the same heat loss: L = (P₂ − P₁) ÷ (difference in mass per second)

Ideal gases

The mole

number of particles = amount × Avogadro constant (N = nN_A), N_A = 6.02 × 10²³ mol⁻¹
amount = mass ÷ molar mass (n = m/M)
mass of one particle = molar mass ÷ N_A
Molar mass in g mol⁻¹ ÷ 1000 gives kg mol⁻¹
The mole (mol) is an SI base unit; molar mass and N_A have derived units
Equal masses of two substances: number of particles is inversely proportional to molar mass

Equation of state

pressure × volume = amount × molar gas constant × temperature (pV = nRT), R = 8.31 J K⁻¹ mol⁻¹
pressure × volume = number of molecules × Boltzmann constant × temperature (pV = NkT), k = 1.38 × 10⁻²³ J K⁻¹
Boltzmann constant = molar gas constant ÷ Avogadro constant (k = R/N_A)
Fixed mass of gas: p₁V₁/T₁ = p₂V₂/T₂
T must be in kelvin; p in Pa and V in m³ when R or k is used
1 cm³ = 10⁻⁶ m³; 1 dm³ = 10⁻³ m³
Graph of pV against T: straight line through the origin with gradient nR

Kinetic theory of gases

pressure × volume = ⅓ × number of molecules × mass of one molecule × mean-square speed (pV = ⅓Nm<c²>)
Nm is the total mass of the gas, so p = ⅓ρ<c²>, where ρ is the density
Root-mean-square speed: c_r.m.s. = √<c²> (square the speeds, take the mean, then take the square root)
Random motion in three dimensions: <c_x²> = ⅓<c²>
Mean translational kinetic energy of one molecule = (3/2)kT, so ½m<c²> = (3/2)kT, with T in kelvin and k = 1.38 × 10⁻²³ J K⁻¹
c_r.m.s. is proportional to √T and to 1/√m, so doubling T multiplies the speed by √2
Elastic collision with a wall at right angles: change in momentum = 2mv

Thermodynamics

Internal energy

Internal energy = sum of the random kinetic energies and potential energies of the molecules of a system
It is a function of state: the same state always has the same internal energy
Temperature rises → mean kinetic energy of the molecules rises → internal energy rises
Change of state at constant temperature: kinetic energy unchanged, potential energy changes, so internal energy still changes
Ideal gas: potential energy is zero, so internal energy depends only on temperature (and the amount of gas)
Ideal gas: total random kinetic energy of N molecules = N × (3/2)kT = (3/2)nRT, with T in kelvin

The first law of thermodynamics

Work done at constant pressure = pressure × change in volume (W = pΔV), with p in Pa and V in m³
First law: increase in internal energy = energy supplied by heating + work done on the system (ΔU = q + W)
q is positive when energy enters by heating and negative when it leaves
W is positive for a compression (work done on the gas) and negative for an expansion (work done by the gas)
Work done on the gas = −(work done by the gas)
On a p–V graph, the area under the line is the work done
Ideal gas at constant temperature: ΔU = 0, so q = −W. No heating (insulated): q = 0, so ΔU = W. 1 cm³ = 10⁻⁶ m³

Oscillations

Simple harmonic oscillations

Period and frequency: T = 1/f. Angular frequency: ω = 2πf = 2π/T, in rad s⁻¹
Defining equation: acceleration = −(angular frequency)² × displacement (a = −ω²x); maximum acceleration = ω²x₀
Displacement, starting from equilibrium at t = 0: x = x₀ sin ωt (calculator in radians)
Velocity: v = v₀ cos ωt, where the maximum speed v₀ = ωx₀
Speed at displacement x: v = ±ω√(x₀² − x²)
A graph of a against x is a straight line through the origin with gradient −ω²
Phase difference = (time difference ÷ period) × 2π rad, or × 360°

Energy in simple harmonic motion

Total energy = ½ × mass × (angular frequency)² × (amplitude)² (E = ½mω²x₀²), with ω = 2πf
Potential energy at displacement x: E_P = ½mω²x²
Kinetic energy at displacement x: E_K = ½mω²(x₀² − x²)
E_K + E_P = total energy at every instant
Total energy is also the maximum kinetic energy, ½mv₀², with v₀ = ωx₀
E ∝ x₀² and E ∝ f²: doubling the amplitude gives four times the energy
Kinetic energy and potential energy each vary with twice the frequency of the oscillation (period T/2)

Damped and forced oscillations, resonance

Damping: a resistive force removes energy from the oscillation, so the amplitude decreases
Light damping: oscillations continue with decreasing amplitude; the period stays almost the same
Critical damping: no oscillation; displacement falls to zero in the shortest possible time
Heavy damping: no oscillation; displacement falls to zero slowly
Forced oscillations take place at the frequency of the driver, not at the natural frequency
Resonance: driving frequency = natural frequency → maximum amplitude
More damping: resonance peak lower and broader, with the maximum at a slightly lower frequency. Energy ∝ amplitude²

Electric fields

Electric fields and field lines

Electric field strength = force ÷ charge (E = F/q), defined for a positive charge
Force on a charge in a field: F = qE
Unit of E: N C⁻¹, the same as V m⁻¹; in base units kg m s⁻³ A⁻¹
Field direction = direction of the force on a positive charge; lines go from + to −
Isolated point charge: radial field, outwards from a positive charge and inwards to a negative charge
Closer lines = stronger field; lines meet a conducting surface at right angles
Charge of an electron or proton: 1.60 × 10⁻¹⁹ C; acceleration a = qE/m

Uniform electric fields

Field strength = potential difference ÷ plate separation (E = ΔV/Δd), in V m⁻¹, with d in metres
ΔV is the difference between the plate potentials, e.g. +300 V and −200 V gives 500 V
Force on a charge: F = qE = qV/d; acceleration a = qE/m
Positive charges accelerate in the direction of the field; negative charges accelerate opposite to it
Entering at right angles to the field: constant velocity parallel to the plates, constant acceleration across them, parabolic path
Accelerated from rest through a p.d. V: kinetic energy gained = qV = ½mv²
Charged drop held at rest between horizontal plates: qE = mg

Electric force between point charges

Force = (charge 1 × charge 2) ÷ (4πε₀ × distance²) (F = Q₁Q₂/(4πε₀r²))
1/(4πε₀) = 8.99 × 10⁹ N m² C⁻²; ε₀ = 8.85 × 10⁻¹² F m⁻¹
F ∝ 1/r²: twice the distance gives one quarter of the force
Like charges repel; unlike charges attract; the two forces are equal and opposite
Charged sphere, outside point: treat the charge as a point charge at the centre, so r = radius + distance from the surface
1 μC = 10⁻⁶ C; 1 nC = 10⁻⁹ C
Several charges on a line: find each force separately, then add them as vectors

Electric field of a point charge

Field strength = charge ÷ (4πε₀ × distance²) (E = Q/(4πε₀r²)), in N C⁻¹
1/(4πε₀) = 8.99 × 10⁹ N m² C⁻²
E ∝ 1/r², so E₁r₁² = E₂r₂² for the same charge
Direction: away from a positive charge, towards a negative charge
A graph of E against 1/r² is a straight line through the origin with gradient Q/(4πε₀)
Between two like charges the fields oppose; between two unlike charges they add
Charged sphere: r = radius + distance from the surface

Electric potential

Potential of a point charge = charge ÷ (4πε₀ × distance) (V = Q/(4πε₀r)), in volts; note r, not r²
Field strength = −potential gradient (E = −ΔV/Δr)
Potential energy of two point charges: E_P = Qq/(4πε₀r), in joules; keep the signs of the charges
Work done moving a charge q through a potential difference ΔV: W = qΔV
For a single point charge: V = Er, so r = V/E
1/(4πε₀) = 8.99 × 10⁹ N m² C⁻²
Potential is a scalar: add the values with their signs, with no directions

Capacitance

Capacitors and capacitance

capacitance = charge ÷ potential difference (C = Q/V); unit farad, 1 F = 1 C V⁻¹
1 μF = 10⁻⁶ F, 1 nF = 10⁻⁹ F, 1 pF = 10⁻¹² F
In parallel: C = C₁ + C₂ + ... (same V, charges add)
In series: 1/C = 1/C₁ + 1/C₂ + ... (same Q, p.d.s add)
Series capacitors: the smaller capacitance has the larger p.d., because V = Q/C with the same Q
Isolated sphere of radius r: C = 4πε₀r
charge = current × time (Q = It) for charging with a constant current

Energy stored in a capacitor

energy stored = ½ × charge × p.d. (W = ½QV)
W = ½CV² (use when C and V are known)
W = Q² ÷ (2C) (use when Q and C are known)
Energy = area under the graph of p.d. against charge
For a fixed capacitor, energy is proportional to V²: doubling V gives 4 times the energy
Energy released when the p.d. falls from V₁ to V₂ = ½C(V₁² − V₂²)

Discharging a capacitor

time constant = resistance × capacitance (τ = RC); Ω × F = s
x = x₀e^−t/RC, where x is Q, V or I and x₀ is the value at t = 0
After time τ the value is 0.37x₀; after 2τ it is 0.14x₀
Initial current I₀ = V₀ ÷ R
Gradient of the Q against t graph = current at that instant (in size)
ln x = ln x₀ − t/RC, so a graph of ln x against t is a straight line of gradient −1/RC
Time to fall to half: t = RC ln 2 = 0.69RC

Magnetic fields

Concept of a magnetic field

Magnetic fields come from permanent magnets and from moving charges (currents)
Field direction = direction of the force on a north pole = direction a plotting compass points
Lines run from north pole to south pole outside a magnet
Closer lines mean a stronger field (larger flux density)
Uniform field: parallel, equally spaced lines
Field lines never cross, because the field at a point has only one direction
A stationary charge feels electric and gravitational forces but no magnetic force

Force on a current-carrying conductor

force = flux density × current × length × sin θ (F = BIL sin θ), θ is the angle between the wire and the field
Wire perpendicular to the field: F = BIL (maximum). Wire parallel to the field: F = 0
Magnetic flux density = force per unit current per unit length on a wire at right angles to the field (B = F ÷ IL)
Unit of B: tesla, 1 T = 1 N A⁻¹ m⁻¹ = 1 kg A⁻¹ s⁻²
Left hand: First finger = Field, seCond finger = Current, thuMb = Motion (force)
Magnet on a balance: change in reading × g = force on the wire (g = 9.81 N kg⁻¹)

Force on a moving charge

force = flux density × charge × speed × sin θ (F = BQv sin θ), θ is the angle between v and B
Circular path: BQv = mv²/r, so r = mv ÷ (BQ)
Time for one revolution T = 2πm ÷ (BQ), which does not depend on the speed
Hall voltage V_H = BI ÷ (ntq): n = number density of charge carriers, t = thickness of the slice, q = charge of each carrier
Hall probe: V_H is proportional to B for a constant current; the slice must be perpendicular to the field
Semiconductors have a much smaller n than metals, so they give a larger Hall voltage
Velocity selector: qE = Bqv, so v = E ÷ B, with E = V ÷ d between the plates

Magnetic fields due to currents

Straight wire: concentric circles, field weaker further from the wire
Right-hand grip: thumb = current, fingers = field direction
Solenoid: uniform field inside (parallel, equally spaced lines), bar-magnet pattern outside
Looking at the end of a solenoid: anticlockwise current = north pole, clockwise current = south pole
An iron (ferrous) core becomes magnetised and adds its own field, so the flux density increases
Parallel currents in the same direction attract; in opposite directions they repel
The forces on the two wires are equal in size and opposite in direction (Newton's third law), even if the currents differ

Electromagnetic induction

magnetic flux = flux density × area perpendicular to the field (Φ = BA); unit weber, 1 Wb = 1 T m²
If the field makes angle θ with the normal to the area: Φ = BA cos θ
flux linkage = NΦ = NBA
Faraday's law: induced e.m.f. is proportional to the rate of change of flux linkage (E = Δ(NΦ) ÷ Δt in size)
Lenz's law: the induced e.m.f. is in the direction that opposes the change producing it
Straight rod of length L moving at speed v across a field: E = BLv
Larger e.m.f.: faster movement, stronger magnet, more turns, larger area

Alternating currents

Characteristics of alternating currents

x = x₀ sin ωt, where x₀ is the peak value and ω = 2πf = 2π ÷ T (ωt in radians)
frequency = 1 ÷ period (f = 1/T)
I_r.m.s. = I₀ ÷ √2 and V_r.m.s. = V₀ ÷ √2 (sinusoidal only)
mean power = ½ × maximum power = ½I₀²R = ½V₀² ÷ R
mean power = I_r.m.s.V_r.m.s. = I_r.m.s.²R = V_r.m.s.² ÷ R
Peak-to-peak value = 2 × peak value
The current is zero twice in every cycle

Rectification and smoothing

Half-wave: one hump per cycle, then a gap of half a period. 50 Hz gives 50 humps per second
Full-wave: two humps per cycle, no gaps. 50 Hz gives 100 humps per second
Bridge rectifier: two diodes conduct in each half-cycle, diagonally opposite pairs in turn
Smoothing capacitor goes in parallel with (across) the load resistor
Ripple is smaller when the time constant RC is much larger than the time between peaks
Less ripple: larger capacitance, larger load resistance, or full-wave instead of half-wave
Between peaks: V = V₀e^−t/RC

Quantum physics

Energy and momentum of a photon

photon energy = Planck constant × frequency (E = hf), h = 6.63 × 10⁻³⁴ J s
E = hc ÷ λ, using c = fλ with c = 3.00 × 10⁸ m s⁻¹
1 eV = 1.60 × 10⁻¹⁹ J. J to eV: divide by 1.60 × 10⁻¹⁹. eV to J: multiply
photon momentum = energy ÷ speed of light (p = E/c = h/λ)
number of photons per second = power ÷ energy of one photon
Force on a surface that absorbs a beam completely = power ÷ c
Higher frequency (shorter wavelength) means more energy and more momentum per photon

Photoelectric effect

photon energy = Planck constant × frequency (E = hf = hc/λ)
photon energy = work function + maximum kinetic energy (hf = Φ + ½mv_max²)
Threshold frequency f₀ = Φ/h; threshold wavelength λ₀ = hc/Φ. Emission needs f ≥ f₀, which means λ ≤ λ₀.
Maximum kinetic energy depends on frequency only, not on intensity.
Photoelectric current is proportional to intensity (at constant frequency above the threshold).
1 eV = 1.60 × 10⁻¹⁹ J. Change Φ into joules before using it with h.
Graph of maximum kinetic energy against frequency: gradient = h, intercept on the frequency axis = f₀.

Wave-particle duality

de Broglie wavelength = Planck constant ÷ momentum (λ = h/p = h/mv)
Evidence for the wave nature of light: interference, diffraction.
Evidence for the particle nature of light: the photoelectric effect.
Evidence for the wave nature of particles: electron diffraction.
Faster electrons (larger accelerating p.d.) have more momentum, a shorter wavelength and smaller diffraction rings.
For an electron accelerated from rest through a p.d. V: eV = ½mv², so p = √(2meV).
Everyday objects have such a large momentum that λ is far too small for wave effects to be seen.

Energy levels in atoms and line spectra

photon energy = difference between the two energy levels (hf = E₁ − E₂)
hf = hc/λ, so a larger energy difference gives a shorter wavelength.
Emission: electron moves to a lower level and a photon is emitted.
Absorption: electron moves to a higher level; the photon energy must match the difference exactly.
Dark absorption lines are at the same wavelengths as the bright emission lines of the same gas.
The absorbed photons are re-emitted in all directions, so those wavelengths are weaker in the original direction.
Number of possible emission lines for n levels = n(n − 1)/2.

Nuclear physics

Mass defect and nuclear binding energy

energy = mass × (speed of light)² (E = mc²); energy released = c²Δm
Mass defect = total mass of the separate nucleons − mass of the nucleus.
Binding energy = mass defect × c²: the minimum energy needed to separate the nucleons to infinity.
In a nuclear equation both nucleon number (top) and proton number (bottom) are conserved.
Fission: a heavy nucleus splits into two lighter nuclei of similar size, usually with a few neutrons.
Fusion: two light nuclei join to form a heavier nucleus.
Energy released = total binding energy after − total binding energy before. 1 u = 1.66 × 10⁻²⁷ kg; 1 MeV = 1.60 × 10⁻¹³ J.

Radioactive decay

activity = decay constant × number of undecayed nuclei (A = λN); activity is measured in becquerel, 1 Bq = 1 decay per second
Decay constant: the probability that a nucleus decays per unit time.
Half-life: the time taken for the number of undecayed nuclei (or the activity) to fall to half its value.
decay constant = 0.693 ÷ half-life (λ = 0.693/t_½)
x = x₀e^−λt, where x is activity, number of undecayed nuclei or count rate.
After n half-lives the fraction remaining is (½)ⁿ.
A graph of ln x against t is a straight line of gradient −λ.

Medical physics

Production and use of ultrasound

specific acoustic impedance = density × speed of sound in the medium (Z = ρc), unit kg m⁻² s⁻¹
intensity reflection coefficient: I_R/I₀ = (Z₁ − Z₂)² ÷ (Z₁ + Z₂)²
Fraction transmitted = 1 − I_R/I₀.
Attenuation: I = I₀e^−μx, where μ is the attenuation (absorption) coefficient and x the distance travelled.
Depth of a boundary = speed × echo time ÷ 2, because the pulse travels there and back.
Gel is used because air and skin have very different Z, so almost all the ultrasound would be reflected at the skin.
Pulses are used so that the transducer can detect echoes between pulses.

Production and use of X-rays

maximum photon energy = electron charge × accelerating p.d. (eV = hc/λ_min), so λ_min = hc/eV
Larger p.d.: shorter minimum wavelength, more penetrating X-rays.
Larger tube current: more electrons per second, greater intensity, same minimum wavelength.
Attenuation: I = I₀e^−μx, where μ is the linear attenuation coefficient.
Good contrast needs tissues with very different attenuation coefficients.
A contrast medium such as barium absorbs X-rays strongly, so soft organs that hold it show up.
Half-value thickness x_½ = 0.693/μ; each such thickness halves the intensity.

PET scanning

Annihilation: a particle meets its antiparticle and their mass is converted into energy as photons.
Mass-energy and momentum are both conserved in annihilation.
For an electron-positron pair at rest: energy of each photon = m_ec² = 8.2 × 10⁻¹⁴ J = 0.51 MeV.
Total energy released = 2m_ec², shared equally between the two photons.
Initial momentum is about zero, so the two photons have equal momentum in opposite directions.
In β⁺ decay a proton in the nucleus changes into a neutron and a positron is emitted.
Difference in distance travelled by the two photons = c × difference in arrival times.

Astronomy and cosmology

Standard candles

radiant flux intensity = luminosity ÷ (4π × distance²) (F = L/(4πd²))
Luminosity L is in W; radiant flux intensity F is in W m⁻²; distance d is in m.
Rearranged for distance: d = √(L/(4πF)).
For the same luminosity, F is proportional to 1/d².
For the same F, L is proportional to d².
Standard candle: an object of known luminosity, for example a Cepheid variable star or a type Ia supernova.
The law assumes the star radiates equally in all directions and nothing absorbs the radiation on the way.

Stellar radii

Wien's displacement law: peak wavelength is proportional to 1 ÷ temperature (λ_max ∝ 1/T)
λ_maxT = constant = 2.9 × 10⁻³ m K (the value is given in the question).
Stefan-Boltzmann law: luminosity = 4π × σ × radius² × temperature⁴ (L = 4πσr²T⁴)
σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; T must be in kelvin.
Radius: r = √(L/(4πσT⁴)).
Double T at the same radius: L is 16 times larger. Double r at the same T: L is 4 times larger.

Hubble's law and the Big Bang theory

redshift: change in wavelength ÷ wavelength ≈ change in frequency ÷ frequency ≈ speed ÷ speed of light (Δλ/λ ≈ Δf/f ≈ v/c)
λ and f here are the values measured in the laboratory (emitted values); the formula holds for v much less than c.
Moving away: wavelength increases, frequency decreases (redshift). Moving towards: the opposite (blueshift).
Δλ/λ is the same for every line in the spectrum of one galaxy.
Hubble's law: recession speed ≈ Hubble constant × distance (v ≈ H₀d)
In SI units H₀ is in s⁻¹ (about 2.2 × 10⁻¹⁸ s⁻¹), v in m s⁻¹, d in m.
1/H₀ is an estimate of the age of the Universe.