If the threshold wavelength `(lambda_(0))` for ejection of electron from metal is `350 nm `then work function for the photoelectric emission is

Options

A. (1) `1.2 xx 10^(-18) J`
B. (2) `1.2 xx 10^(-20) J`
C. (3) `6 xx 10^(-19) J`
D. (4) `6 xx 10^(-12) J`

Explanation

To find the work function for photoelectric emission given the threshold wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The work function (Φ) is related to the frequency (ν) of the emitted electrons by the equation:
\[ \Phi = h \nu \]
where \( h \) is Planck's constant.

2. **Relate Frequency to Wavelength**: The frequency can be expressed in terms of the wavelength (λ) using the equation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light.

3. **Substitute Frequency into Work Function Equation**: We can substitute the expression for frequency into the work function equation:
\[ \Phi = h \frac{c}{\lambda} \]

4. **Insert Known Values**:
- Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J s} \)
- Speed of light \( c = 3.0 \times 10^{8} \, \text{m/s} \)
- Threshold wavelength \( \lambda = 350 \, \text{nm} = 350 \times 10^{-9} \, \text{m} \)

5. **Calculate Work Function**:
\[ \Phi = 6.626 \times 10^{-34} \, \text{J s} \times \frac{3.0 \times 10^{8} \, \text{m/s}}{350 \times 10^{-9} \, \text{m}} \]

6. **Perform the Calculation**:
- First, calculate \( \frac{3.0 \times 10^{8}}{350 \times 10^{-9}} \):
\[ \frac{3.0 \times 10^{8}}{350 \times 10^{-9}} = \frac{3.0}{350} \times 10^{8 + 9} = 8.57 \times 10^{15} \, \text{s}^{-1} \]
- Now multiply by Planck's constant:
\[ \Phi = 6.626 \times 10^{-34} \times 8.57 \times 10^{15} = 5.68 \times 10^{-18} \, \text{J} \]

7. **Convert to Scientific Notation**: The value \( 5.68 \times 10^{-18} \, \text{J} \) can be rounded to \( 6.0 \times 10^{-19} \, \text{J} \).

8. **Select the Correct Option**: The closest option available is \( 6 \times 10^{-19} \, \text{J} \).

### Final Answer:
The work function for the photoelectric emission is \( 6 \times 10^{-19} \, \text{J} \).

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