The threshold wavelength for ejection of electrons from a metal is 450 nm. The work function for the photoelectric emission from the metal is

Options

A. 5.6×`10^(−19)`J
B. 4.4×`10^(−19)`J
C. 7.6×`10^(−19)`J
D. 4.4×`10^(−20)`J

Explanation

To find the work function for photoelectric emission from the metal, we can follow these steps:

### Step 1: Understand the relationship between work function and threshold wavelength
The work function (W) in the photoelectric effect is given by the equation:
\[ W = h \nu_0 \]
where \( \nu_0 \) is the threshold frequency.

### Step 2: Relate threshold frequency to threshold wavelength
The threshold frequency \( \nu_0 \) can be expressed in terms of the threshold wavelength \( \lambda_0 \) using the equation:
\[ \nu_0 = \frac{c}{\lambda_0} \]
where \( c \) is the speed of light.

### Step 3: Substitute the threshold wavelength
Given that the threshold wavelength \( \lambda_0 \) is 450 nm, we need to convert this into meters:
\[ \lambda_0 = 450 \, \text{nm} = 450 \times 10^{-9} \, \text{m} \]

### Step 4: Calculate the threshold frequency
Now, we can calculate the threshold frequency using the speed of light \( c = 3 \times 10^8 \, \text{m/s} \):
\[ \nu_0 = \frac{c}{\lambda_0} = \frac{3 \times 10^8 \, \text{m/s}}{450 \times 10^{-9} \, \text{m}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \nu_0 = \frac{3 \times 10^8}{450 \times 10^{-9}} \]
\[ \nu_0 = \frac{3 \times 10^8}{4.5 \times 10^{-7}} \]
\[ \nu_0 = \frac{3}{4.5} \times 10^{15} \]
\[ \nu_0 = 0.6667 \times 10^{15} \, \text{Hz} \]
\[ \nu_0 \approx 6.67 \times 10^{14} \, \text{Hz} \]

### Step 6: Calculate the work function
Now we can substitute \( \nu_0 \) back into the work function equation:
\[ W = h \nu_0 \]
Using Planck's constant \( h = 6.626 \times 10^{-34} \, \text{Js} \):
\[ W = 6.626 \times 10^{-34} \, \text{Js} \times 6.67 \times 10^{14} \, \text{Hz} \]

### Step 7: Perform the final calculation
Calculating the work function:
\[ W \approx 4.41 \times 10^{-19} \, \text{J} \]

### Conclusion
The work function for photoelectric emission from the metal is approximately:
\[ W \approx 4.41 \times 10^{-19} \, \text{J} \]