The threshold wavelength for ejection of electrons from a metal is 650 nm. The work function for the photoelectric emission from the metal is

Options

A. 7.6×`10^(−19)`J
B. 3×`10^(−19)`J
C. 4.6×`10^(−19)`J
D. 6×`10^(−19)`J

Explanation

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

### Step 1: Understand the relationship between work function and wavelength
The work function \( W \) is related to the threshold wavelength \( \lambda_0 \) by the equation:
\[ W = \frac{hc}{\lambda_0} \]
where:
- \( W \) is the work function,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda_0 \) is the threshold wavelength.

### Step 2: Convert the threshold wavelength to meters
The given threshold wavelength is \( 650 \, \text{nm} \). We need to convert this to meters:
\[ \lambda_0 = 650 \, \text{nm} = 650 \times 10^{-9} \, \text{m} \]

### Step 3: Substitute the values into the work function equation
Now we can substitute the values of \( h \), \( c \), and \( \lambda_0 \) into the equation:
\[ W = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{650 \times 10^{-9} \, \text{m}} \]

### Step 4: Calculate the work function
Now, we perform the calculation:
\[ W = \frac{(6.626 \times 10^{-34}) \times (3 \times 10^8)}{650 \times 10^{-9}} \]
Calculating the numerator:
\[ 6.626 \times 10^{-34} \times 3 \times 10^8 = 1.9878 \times 10^{-25} \, \text{Js} \]
Now, dividing by the denominator:
\[ W = \frac{1.9878 \times 10^{-25}}{650 \times 10^{-9}} = \frac{1.9878 \times 10^{-25}}{6.5 \times 10^{-7}} \approx 3.06 \times 10^{-19} \, \text{J} \]

### Step 5: Final result
Thus, the work function for the photoelectric emission from the metal is approximately:
\[ W \approx 3.06 \times 10^{-19} \, \text{J} \]

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