Search any question & find its solution
Question:
Answered & Verified by Expert
The maximum velocities of the photoelectrons ejected are $v$ and $2 v$ for the incident light of wavelength $400 \mathrm{~nm}$ and $250 \mathrm{~nm}$ on a metal surface respectively. The work function of the metal in terms of Planck's constant $h$ and velocity of light $c$ is
Options:
Solution:
1227 Upvotes
Verified Answer
The correct answer is:
$2 h c \times 10^6 \mathrm{~J}$
As per question
Solving eqns. (i) and (ii), we get
$\begin{aligned} & \frac{h c}{250 \mathrm{~nm}}-\phi_0=\frac{4 h c}{400 \mathrm{~nm}}-4 \phi_0 \\ & \text { or } \phi_0=\frac{h c}{500 \times 10^{-9}} \mathrm{~J}=\frac{10^9 h c}{500} \mathrm{~J}=\frac{1000 h c}{500} \times 10^6 \mathrm{~J}\end{aligned}$
$=2 h c \times 10^6 \mathrm{~J}$
Solving eqns. (i) and (ii), we get
$\begin{aligned} & \frac{h c}{250 \mathrm{~nm}}-\phi_0=\frac{4 h c}{400 \mathrm{~nm}}-4 \phi_0 \\ & \text { or } \phi_0=\frac{h c}{500 \times 10^{-9}} \mathrm{~J}=\frac{10^9 h c}{500} \mathrm{~J}=\frac{1000 h c}{500} \times 10^6 \mathrm{~J}\end{aligned}$
$=2 h c \times 10^6 \mathrm{~J}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.