Question

The work function of three photosensitive materials used to build photoelectric devices are given as : Sodium ( $2.75\, eV$ ), copper $(4.65\, eV )$ and gold $(5.1\, eV )$. Which of the following statements is correct. (The frequency of visible light lies in the range $4 \times 10^{14}\, Hz$ to $8 \times 10^{14}\, Hz$ )

• A. Devices built by copper and gold can operate with visible light
• B. Devices built using sodium can operate with ultraviolet light
• C. All the devices can operate with infrared light
• D. All the devices can operate with visible light
• E. No device can operate with visible light

Answer 1

Answer: (B)

Given, work function are as,
$W_{N a}=2.75\, eV $
$W_{C u}=4.65\, eV$
and $W_{A u}=5. 1\, eV$
The frequency range of visible light $4 \times 10^{14}\, Hz$ to $8 \times 10^{14}\, Hz$, so the maximum energy of photon and minimum energy of photon in visible light.
$E_{\max } =\frac{6.63 \times 10^{-34} \times 8 \times 10^{14}}{1.6 \times 10^{-19}} (\because E=h v) $
$=3.31\, eV$
Similarly, $E_{\min } =\frac{6.63 \times 10^{-34} \times 4 \times 10^{14}}{1.6 \times 10^{-19}} $
$=1.65\, eV$
Now, comparing the work function of above mentioned metal with $E_{\max }$. We get only sodium device can give photoelectron.
Further sodium device can also work with photons of higher energy then $2.75\, eV$ like $x$ -rays, UV rays etc.