A sodium metal piece is illuminated with light of wavelength 0.3 `mum`. The work function of sodium is 2.46 eV. For this situation ,mark out the correct statement (s).

Options

A. The maximum kinetic energy of the ejected photoelectrons is 1.68 eV
B. The cut-off wavelength for sodium is 505 nm
C. The minimum photon energy of incident light for photoelectric effect to take place is 2.46 eV
D. All of the above

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Energy of Incident Light
We start by calculating the energy of the incident light using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{J s} \)
- \( c \) (speed of light) = \( 3.00 \times 10^{8} \, \text{m/s} \)
- \( \lambda \) (wavelength) = \( 0.3 \, \mu m = 0.3 \times 10^{-6} \, m \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.00 \times 10^{8} \, \text{m/s})}{0.3 \times 10^{-6} \, m} \]

Calculating the energy:
\[ E = \frac{1.9878 \times 10^{-25}}{0.3 \times 10^{-6}} = 6.626 \times 10^{-19} \, \text{J} \]

Now, convert this energy from joules to electron volts (1 eV = \( 1.6 \times 10^{-19} \, \text{J} \)):
\[ E = \frac{6.626 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 4.14 \, \text{eV} \]

### Step 2: Calculate the Maximum Kinetic Energy of Ejected Electrons
Using Einstein's photoelectric equation:
\[ K.E. = E - \phi \]
Where \( \phi \) (work function of sodium) = 2.46 eV.

Substituting the values:
\[ K.E. = 4.14 \, \text{eV} - 2.46 \, \text{eV} = 1.68 \, \text{eV} \]

### Step 3: Calculate the Cutoff Wavelength
The cutoff wavelength \( \lambda_0 \) can be calculated using the work function:
\[ \phi = \frac{hc}{\lambda_0} \]
Rearranging gives:
\[ \lambda_0 = \frac{hc}{\phi} \]

Substituting the values:
\[ \lambda_0 = \frac{(6.626 \times 10^{-34} \, \text{J s})(3.00 \times 10^{8} \, \text{m/s})}{2.46 \times 1.6 \times 10^{-19} \, \text{J}} \]

Calculating:
\[ \lambda_0 = \frac{1.9878 \times 10^{-25}}{3.936 \times 10^{-19}} \approx 5.05 \times 10^{-7} \, m = 505 \, nm \]

### Step 4: Determine the Minimum Photon Energy
The minimum photon energy required for the photoelectric effect to occur is equal to the work function:
\[ E_{min} = \phi = 2.46 \, \text{eV} \]

### Conclusion
Based on the calculations:
1. The maximum kinetic energy of ejected electrons is \( 1.68 \, \text{eV} \) (Correct).
2. The cutoff wavelength of sodium is \( 505 \, nm \) (Correct).
3. The minimum photon energy for the photoelectric effect is \( 2.46 \, \text{eV} \) (Correct).

Thus, all statements are correct.