Dual Nature of Radiation and Matter - Result Question 50

52. The work functions for metals $A, B$ and $C$ are respectively $1.92 eV, 2.0 eV$ and $5 eV$. According to Einstein’s equation, the metals which will emit photoelectrons for a radiation of wavelength $4100 \AA$ is/are

[2005]

(a) none

(b) A only

(c) A and B only

(d) all three metals

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Answer:

Correct Answer: 52. (c)

Solution:

(c) $E=\frac{h c}{\lambda}$ $\Rightarrow E=\frac{12375}{\lambda(\text{ in } A)} eV \Rightarrow E=\frac{12375}{4100} eV$

$\Rightarrow E \approx 3 eV$

So, only metals having work function less than $3 eV$ can emit photoelectrons for the incident radiation of wavelength $4100 \AA$.

(a) K.E. $=h v-\phi$

$\therefore$ graph of K.E. versus $v$ is a straight line with $+v e$ slope $h$ and K.E. $>0$ for $v$ such that $h v>\phi$.