Question

A certain meal when irradiated by light $(v=3.2\times {10}^{16}Hz)$ emits photoelectrons with twice K.E. as did photoelectrons when the same metal is irradiated by light $(v=2.1\times {10}^{16}Hz)$. The $v_0$ of the metal is:

• A. $1.2\times {10}^{14}Hz$
• B. $8\times {10}^{15}Hz$
• C. $1.2\times {10}^{16}Hz$
• D. $4\times {10}^{12}Hz$

Answer 1

Answer: (B)

$8\times {10}^{15}Hz$

A given metal has characteristic threshold frequency (${\nu }_0$) for photoelectric effect. The energy other than work function ($h{\nu }_0$) is the kinetic energy of the photoelectron.

where, $h=6.626\times {10}^{-34}Js$

${\nu }_1=3.2\times {10}^{16}Hz,{\nu }_2=2\times {10}^{16}Hz$

$(K.E.{)}_1=h{\nu }_1-h{\nu }_0$

$(K.E.{)}_2=h{\nu }_2-h{\nu }_0$

As $(K.E.{)}_1=2\times (K.E.{)}_2$

$\therefore (h{\nu }_1-h{\nu }_0)=2(h{\nu }_2-h{\nu }_0)$

or ${\nu }_0=2{\nu }_2-{\nu }_1$

$=2\times (2\times {10}^{16})-(3.2\times {10}^{16})$

$=0.8\times {10}^{16}=8\times {10}^{15}Hz$

option B