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Modern Physics formulas

Master Modern Physics through 38 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Modern Physics, every formula

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Photon energy
$E = h ν = \frac{h c}{λ}$
Q1MCQPhoton energy
The energy of a photon is:
- A
  $\dfrac{hc}{\lambda}$
- B
  $\dfrac{h\lambda}{c}$
- C
  $hc\lambda$
- D
  $\dfrac{\lambda}{hc}$
Photon energy (eV)
$E = \frac{1240}{λ ( nm )} eV$
Photon momentum
$p = \frac{h}{λ} = \frac{E}{c}$
Q1MCQPhoton momentum
The momentum of a photon is:
- A
  $\dfrac{h}{\lambda}$
- B
  $h\lambda$
- C
  $\dfrac{\lambda}{h}$
- D
  $hc$
Photoelectric equation
$h ν = ϕ + K_{m a x}$
Q1MCQPhotoelectric equation
Einstein's photoelectric equation is:
- A
  $h\nu=\phi+K_{\max}$
- B
  $h\nu=\phi-K_{\max}$
- C
  $K_{\max}=\phi$
- D
  $h\nu=K_{\max}$
Work function
$ϕ = h ν_{0} = \frac{h c}{λ _{0}}$
Q1MCQWork function
The work function of a metal is:
- A
  $\dfrac{hc}{\lambda_0}$
- B
  $\dfrac{hc}{\lambda}$
- C
  $h\nu$
- D
  $eV_s$
Max KE (stopping potential)
$K_{m a x} = e V_{s}$
Q1MCQStopping potential
The maximum kinetic energy of photoelectrons equals:
- A
  $eV_s$
- B
  $\dfrac{V_s}{e}$
- C
  $h\nu$
- D
  $\phi$
Threshold wavelength
$λ_{0} = \frac{h c}{ϕ}$
Q1MCQThreshold wavelength
The threshold wavelength is:
- A
  $\dfrac{hc}{\phi}$
- B
  $\dfrac{\phi}{hc}$
- C
  $hc\phi$
- D
  $\dfrac{h}{\phi}$
Quantum efficiency
$η = \frac{n _{e}}{n _{p h}}$
Q1MCQQuantum efficiency
The quantum efficiency of a photocell is:
- A
  $\dfrac{n_e}{n_{ph}}$
- B
  $\dfrac{n_{ph}}{n_e}$
- C
  $n_e n_{ph}$
- D
  $1$
De Broglie wavelength
$λ = \frac{h}{p} = \frac{h}{m v}$
Q1MCQDe Broglie
The de Broglie wavelength of a particle is:
- A
  $\dfrac{h}{mv}$
- B
  $\dfrac{mv}{h}$
- C
  $hmv$
- D
  $\dfrac{h}{m}$
De Broglie (accelerated charge)
$λ = \frac{h}{2 m q V}$
Q1MCQAccelerated charge
For a charge $q$ accelerated through $V$, the de Broglie wavelength is:
- A
  $\dfrac{h}{\sqrt{2mqV}}$
- B
  $\dfrac{h}{\sqrt{mqV}}$
- C
  $\dfrac{h}{2mqV}$
- D
  $h\sqrt{2mqV}$
De Broglie (electron)
$λ = \frac{12.27}{V} \overset{˚}{A}$
V in volts
Q1MCQElectron wavelength
The de Broglie wavelength of an electron accelerated through $V$ volts is:
- A
  $\dfrac{12.27}{\sqrt{V}}$ \AA
- B
  $\dfrac{12.27}{V}$ \AA
- C
  $12.27\sqrt{V}$ \AA
- D
  $\dfrac{0.286}{\sqrt{V}}$ \AA
Radiation pressure
$P = (1 + r) \frac{I}{c}$
Q1MCQRadiation pressure
The radiation pressure of a beam (reflectivity $r$) is:
- A
  $(1+r)\dfrac{I}{c}$
- B
  $\dfrac{I}{c}$
- C
  $rI$
- D
  $\dfrac{I}{2c}$
Intensity of light
$I = \frac{P}{A} = \frac{nh ν}{A}$
Q1MCQLight intensity
The intensity of light in terms of photon rate is:
- A
  $\dfrac{n h\nu}{A}$
- B
  $\dfrac{h\nu}{A}$
- C
  $n h\nu$
- D
  $\dfrac{A}{n h\nu}$
Bohr radius
$r_{n} = 0.529 \frac{n ^{2}}{Z} \overset{˚}{A}$
Q1MCQBohr radius
The radius of the $n$th Bohr orbit is:
- A
  $0.529\,\dfrac{n^{2}}{Z}$ \AA
- B
  $0.529\,\dfrac{Z}{n^{2}}$ \AA
- C
  $0.529\,n^{2}Z$ \AA
- D
  $0.529\,n$ \AA
Bohr velocity
$v_{n} = 2.18 \times 1 0^{6} \frac{Z}{n} m/s$
Q1MCQBohr velocity
The velocity in the $n$th Bohr orbit varies as:
- A
  $\dfrac{Z}{n}$
- B
  $\dfrac{n}{Z}$
- C
  $\dfrac{Z}{n^{2}}$
- D
  $nZ$
Bohr energy
$E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}} eV$
Angular momentum (Bohr)
$m v r = \frac{nh}{2 π}$
Q1MCQAngular momentum
Bohr's quantization of angular momentum gives:
- A
  $mvr=\dfrac{nh}{2\pi}$
- B
  $mvr=nh$
- C
  $mvr=\dfrac{h}{2\pi}$
- D
  $mvr=\dfrac{n}{2\pi}$
KE and PE (Bohr)
$K = ∣ E_{n} ∣, U = 2 E_{n}$
Q1MCQKE and PE
In a Bohr atom, the potential energy equals:
- A
  $2E_n$
- B
  $-E_n$
- C
  $E_n$
- D
  $\tfrac12 E_n$
Rydberg formula
$\frac{1}{λ} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$
Q1MCQRydberg formula
The wavelength of a spectral line is given by:
- A
  $\dfrac{1}{\lambda}=RZ^{2}\left(\dfrac{1}{n_1^{2}}-\dfrac{1}{n_2^{2}}\right)$
- B
  $\lambda=R\left(\dfrac{1}{n_1}-\dfrac{1}{n_2}\right)$
- C
  $\dfrac{1}{\lambda}=R(n_1-n_2)$
- D
  $\lambda=RZ^{2}$
Ionization energy
$E_{i o n} = 13.6 Z^{2} eV$
Number of spectral lines
$N = \frac{n ( n - 1 )}{2}$
Continuous X-ray cutoff
$λ_{m i n} = \frac{12400}{V ( volts )} \overset{˚}{A}$
Q1MCQX-ray cutoff
The minimum wavelength of continuous X-rays is:
- A
  $\dfrac{12400}{V}$ \AA
- B
  $12400\,V$ \AA
- C
  $\dfrac{V}{12400}$ \AA
- D
  $\dfrac{1240}{V}$ \AA
Moseley's law
$ν = a (Z - b)$
Q1MCQMoseley's law
Moseley's law for characteristic X-rays is:
- A
  $\sqrt{\nu}=a(Z-b)$
- B
  $\nu=a(Z-b)$
- C
  $\sqrt{\nu}=aZ^{2}$
- D
  $\nu=\dfrac{a}{Z}$
Bragg's law
$2 d sin θ = nλ$
Q1MCQBragg's law
Bragg's law for X-ray diffraction is:
- A
  $2d\sin\theta=n\lambda$
- B
  $d\sin\theta=n\lambda$
- C
  $2d\cos\theta=n\lambda$
- D
  $d=n\lambda$
X-ray absorption
$I = I_{0} e^{- μx}$
Q1MCQX-ray absorption
The intensity of X-rays after thickness $x$ is:
- A
  $I_0 e^{-\mu x}$
- B
  $I_0 e^{\mu x}$
- C
  $I_0(1-e^{-\mu x})$
- D
  $I_0\mu x$
Nuclear radius
$R = R_{0} A^{1/3}, R_{0} = 1.2 fm$
Q1MCQNuclear radius
The nuclear radius varies as:
- A
  $A^{1/3}$
- B
  $A$
- C
  $A^{2/3}$
- D
  $A^{2}$
Mass defect
$Δ m = [Z m_{p} + (A - Z) m_{n}] - M$
Q1MCQMass defect
The mass defect of a nucleus is:
- A
  $[Zm_p+(A-Z)m_n]-M$
- B
  $M-Zm_p$
- C
  $Zm_p+(A-Z)m_n$
- D
  $M$
Binding energy
$B E = Δ m \times 931.5 MeV$
Q1MCQBinding energy
The binding energy in terms of mass defect is:
- A
  $\Delta m\times931.5$ MeV
- B
  $\Delta m\times c$
- C
  $\dfrac{\Delta m}{931.5}$
- D
  $\Delta m^{2}$
Binding energy per nucleon
$\frac{B E}{A}$
Q1MCQBE per nucleon
Nuclear stability is highest when the binding energy per nucleon is:
- A
  maximum
- B
  minimum
- C
  zero
- D
  negative
Radioactive decay law
$N = N_{0} e^{- λ t}$
Q1MCQDecay law
The number of undecayed nuclei at time $t$ is:
- A
  $N_0 e^{-\lambda t}$
- B
  $N_0 e^{\lambda t}$
- C
  $N_0(1-e^{-\lambda t})$
- D
  $N_0\lambda t$
Half-life
$T_{1/2} = \frac{0.693}{λ}$
Q1MCQHalf-life
The half-life is related to the decay constant by:
- A
  $\dfrac{0.693}{\lambda}$
- B
  $0.693\lambda$
- C
  $\dfrac{\lambda}{0.693}$
- D
  $\dfrac{1}{\lambda}$
Mean (average) life
$τ = \frac{1}{λ} = 1.44 T_{1/2}$
Q1MCQMean life
The mean life of a radioactive sample is:
- A
  $\dfrac{1}{\lambda}=1.44\,T_{1/2}$
- B
  $\dfrac{0.693}{\lambda}$
- C
  $\lambda$
- D
  $0.693\,T_{1/2}$
Nuclei after n half-lives
$N = \frac{N _{0}}{2 ^{n}}, n = \frac{t}{T _{1/2}}$
Activity
$A = λ N = A_{0} e^{- λ t}$
Q1MCQActivity
The activity of a sample is:
- A
  $\lambda N$
- B
  $\dfrac{N}{\lambda}$
- C
  $\lambda$
- D
  $N^{2}$
Alpha decay
$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He$
Q1MCQAlpha decay
In alpha decay, the atomic number changes by:
- A
  $-2$
- B
  $+1$
- C
  $-1$
- D
  $+2$
Beta-minus decay
$_{Z}^{A} X \to_{Z + 1}^{A} Y + β^{-} + \overset{ν}{ˉ}$
Q1MCQBeta decay
In $\beta^{-}$ decay, the atomic number changes by:
- A
  $+1$
- B
  $-1$
- C
  $-2$
- D
  $0$
Effective half-life
$\frac{1}{T} = \frac{1}{T _{1}} + \frac{1}{T _{2}}$
Q1MCQEffective half-life
For two decay modes, the effective half-life satisfies:
- A
  $\dfrac{1}{T}=\dfrac{1}{T_1}+\dfrac{1}{T_2}$
- B
  $T=T_1+T_2$
- C
  $T=\sqrt{T_1 T_2}$
- D
  $T=T_1 T_2$
Mass–energy (1 amu)
$1 amu = 931.5 MeV / c^{2}$

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Modern Physics formulas

Modern Physics, every formula

Photon energy

Photon energy (eV)

Photon momentum

Photoelectric equation

Work function

Max KE (stopping potential)

Threshold wavelength

Quantum efficiency

De Broglie wavelength

De Broglie (accelerated charge)

De Broglie (electron)

Radiation pressure

Intensity of light

Bohr radius

Bohr velocity

Bohr energy

Angular momentum (Bohr)

KE and PE (Bohr)

Rydberg formula

Ionization energy

Number of spectral lines

Continuous X-ray cutoff

Moseley's law

Bragg's law

X-ray absorption

Nuclear radius

Mass defect

Binding energy

Binding energy per nucleon

Radioactive decay law

Half-life

Mean (average) life

Nuclei after n half-lives

Activity

Alpha decay

Beta-minus decay

Effective half-life

Mass–energy (1 amu)

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