SATHEE: Shortcut Methods

JEE Main

Numerical	Shortcut Method
An electron is accelerated through a potential difference of 100 V. Calculate its de Broglie wavelength.	De Broglie equation: $λ = \frac{h}{\sqrt{2 m e V}}$
A beam of monochromatic light with a wavelength of 600 nm strikes a metal surface. Calculate the maximum kinetic energy of the emitted electrons.	Einstein’s photoelectric effect equation: $K E_{m a x} = h ν - ϕ$

A hydrogen atom is in the n = 2 energy level. Calculate the wavelength of the photon emitted when the atom transitions to the n = 1 energy level.	Rydberg formula: $\frac{1}{λ} = R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$
A nucleus with a mass number of 238 undergoes alpha decay. Calculate the energy released in the process.	Alpha decay energy formula: $E = - [(M_{p} + M_{α}) c^{2} - M_{d}] c^{2}$

A neutron is captured by a nucleus with a mass number of 239. Calculate the number of neutrons and protons in the resulting nucleus.	The number of protons remains the same while the number of neutrons increases by 1 in the resulting nucleus.

CBSE Board Exams

Numerical	Shortcut Method
An electron has a de Broglie wavelength of 0.1 nm. Calculate its kinetic energy	De Broglie equation: $λ = \frac{h}{\sqrt{2 m e K}}$
A beam of monochromatic light with a frequency of 5 x 10¹⁴ Hz strikes a metal surface. Calculate the maximum kinetic energy of the emitted electrons	Einstein’s photoelectric effect equation: $K E_{m a x} = h ν - ϕ$
A hydrogen atom is in the n = 3 energy level. Calculate the wavelength of the photon emitted when the atom transitions to the n = 2 energy level	Rydberg formula: $\frac{1}{λ} = R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$
A nucleus with a mass number of 235 undergoes fission. Calculate the energy released in the process	Nuclear Fission formula: $E = [(M_{A}) c^{2} - (M_{C} + M_{D}) c^{2})] c^{2}$
A proton is accelerated through a potential difference of 1000 V. Calculate its de Broglie wavelength	De Broglie equation: $λ = \frac{h}{\sqrt{2 m_{p} c^{2} (Δ V)}}$