Radiation, with wavelength $6561 \text{ Å}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} \text{ T}$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to:

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Modern Physics

Radiation, with wavelength

6561 \overset{˚}{A}

falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of

3 \times 1 0^{- 4} T

. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to:

Answer: (D)

The incident photon carries energy

E = \frac{h c}{λ} = \frac{12400}{6561 A ˚} \approx 1.9 eV

. Inside the magnetic field the most energetic photoelectrons travel on the largest circular arc, so for them

r = \frac{p}{q B}

, giving a momentum

p = q B r = (1.6 \times 1 0^{- 19}) (3 \times 1 0^{- 4}) (10 \times 1 0^{- 3}) = 4.8 \times 1 0^{- 25} kg m s^{- 1}

. Their maximum kinetic energy is

K_{m a x} = \frac{p ^{2}}{2 m} = \frac{( 4.8 \times 1 0 ^{- 25} ) ^{2}}{2 ( 9.1 \times 1 0 ^{- 31} )} \approx 1.27 \times 1 0^{- 19} J \approx 0.8 eV

. Einstein's photoelectric relation

E = ϕ + K_{m a x}

then fixes the work function as

ϕ = E - K_{m a x} = 1.9 - 0.8 \approx 1.1 eV

, since the quantity asked for is the work function and not the ejected electrons' kinetic energy.

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option