A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 10^{14} \mathrm{~Hz}$. The velocity of ejected electron is $\_\_\_\_$ $\times 10^{5} \mathrm{~ms}^{-1}$. (Nearest integer) [Use: $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, \mathrm{m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}$]

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Atomic Structure

A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is

4.3 \times 1 0^{14} Hz

. The velocity of ejected electron is

____

\times 1 0^{5} ms^{- 1}

.
(Nearest integer)
[Use:

h = 6.63 \times 1 0^{- 34} Js, m_{e} = 9.0 \times 1 0^{- 31} kg

]

Answer: 5

The incident radiation has frequency

ν = \frac{c}{λ} = \frac{3 \times 1 0 ^{8}}{500 \times 1 0 ^{- 9}} = 6 \times 1 0^{14} Hz

The energy above the threshold appears as kinetic energy of the ejected electron:

\frac{1}{2} m_{e} v^{2} = h (ν - ν_{0}) = 6.63 \times 1 0^{- 34} \times (6 - 4.3) \times 1 0^{14} = 1.127 \times 1 0^{- 19} J

v = \frac{2 \times 1.127 \times 1 0 ^{- 19}}{9.0 \times 1 0 ^{- 31}} = 2.50 \times 1 0^{11} = 5.0 \times 1 0^{5} m s^{- 1}

The electron is ejected with a speed of

5 \times 1 0^{5} m s^{- 1}

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Integer answer