Q129 / 180 · NEET 2019 (Odisha) · Physics
The work function of a photosensitive material is $4.0 \mathrm{eV}$. This longest wavelength of light that can cause photon emission from the substance is (approximately)
- A$3100 \mathrm{~nm}$
- B$966 \mathrm{~nm}$
- C$31 \mathrm{~nm}$
- Correct answerD$310 \mathrm{~nm}$
Solution
The work function of material is given by
$$
\begin{aligned}
& \phi=\mathrm{hv} \\
& \phi=\frac{\mathrm{hc}}{\lambda}
\end{aligned}
$$
$$
\text { ..(i) }\left[\because v=\frac{c}{\lambda}\right]
$$
where, $\mathrm{h}=$ Planck's constant $=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$
$\mathrm{c}=$ speed of length $=3 \times 10^8 \mathrm{~ms}^{-1}$ and
$\lambda=$ wavelength of light
Here, $\phi=4 \mathrm{eV}=4 \times 1.6 \times 10^{-19} \mathrm{~J}$
Substituting the given values in Eq. (i), we get $\Rightarrow \quad 4 \times 1.6 \times 10^{-19}=\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{\lambda}$
or $\quad \lambda=\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{4 \times 1.6 \times 10^{-19}}$
$=3.108 \times 10^{-7} \mathrm{~m} \simeq 310 \mathrm{~nm}$
Hence, the correct answer is option: 'D'.