JEE MAIN - Physics (2025 - 23rd January Evening Shift - No. 9)
Explanation
Let's break down the problem step by step:
In the photoelectric effect, the energy of a photon is given by:
$$ h\nu = \phi + K_e $$
where:
$$\phi$$ is the work function of the metal,
$$K_e$$ is the kinetic energy of the ejected electron.
The kinetic energy of the ejected electrons is provided by the stopping potential:
$$ K_e = eV $$
Given that the stopping potential is $$ V = 2 \text{ V} $$, we have:
$$ K_e = 2 \text{ eV} $$
Now, we can calculate the photon energy:
$$ h\nu = \phi + K_e = 2.14 \text{ eV} + 2 \text{ eV} = 4.14 \text{ eV} $$
The relation between the photon's energy and its wavelength is:
$$ h\nu = \frac{hc}{\lambda} $$
Rearranging for $$\lambda$$:
$$ \lambda = \frac{hc}{h\nu} $$
Given that $$ hc = 1242 \text{ eV·nm} $$, substitute the values:
$$ \lambda = \frac{1242 \text{ eV·nm}}{4.14 \text{ eV}} $$
Calculate the wavelength:
$$ \lambda \approx \frac{1242}{4.14} \approx 300 \text{ nm} $$
Thus, the wavelength of the incident electromagnetic wave is approximately 300 nm.
The correct answer is Option C: 300 nm.
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