The work function of a substance is 1.6 ev. The longest wavelength of light that can produce potoemisson form the substance is

Options

A. `7750 Å`
B. `3875 Å`
C. `5800 Å`
D. `2900 Å`

Explanation

To solve the problem of finding the longest wavelength of light that can produce photoemission from a substance with a work function of 1.6 eV, we will use the relationship between work function, wavelength, and the constants involved in the photoelectric effect.

### Step-by-Step Solution:

1. **Understand the Work Function**:
The work function (Φ) is the minimum energy required to remove an electron from the surface of a material. It is given as 1.6 eV.

2. **Convert Work Function to Joules**:
Since we will be using the formula that involves energy in joules, we need to convert the work function from electron volts (eV) to joules (J). The conversion factor is:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Therefore,
\[ \Phi = 1.6 \text{ eV} = 1.6 \times 1.6 \times 10^{-19} \text{ J} = 2.56 \times 10^{-19} \text{ J} \]

3. **Use the Formula for Wavelength**:
The energy of a photon can be related to its wavelength (λ) using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \text{ J s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \text{ m/s}\)),
- \(\lambda\) is the wavelength in meters.

4. **Rearranging the Formula**:
To find the wavelength, we rearrange the formula:
\[ \lambda = \frac{hc}{E} \]
Here, \(E\) is the work function in joules.

5. **Substituting the Values**:
Now, substituting the values into the equation:
\[ \lambda = \frac{(6.626 \times 10^{-34} \text{ J s})(3 \times 10^8 \text{ m/s})}{2.56 \times 10^{-19} \text{ J}} \]

6. **Calculating the Wavelength**:
Performing the calculation:
\[ \lambda = \frac{1.9878 \times 10^{-25}}{2.56 \times 10^{-19}} \approx 7.775 \times 10^{-7} \text{ m} \]
To convert this to angstroms (1 angstrom = \(10^{-10}\) m):
\[ \lambda \approx 7.775 \times 10^{-7} \text{ m} \times 10^{10} \text{ angstrom/m} \approx 7750 \text{ angstrom} \]

7. **Final Result**:
Therefore, the longest wavelength of light that can produce photoemission from the substance is approximately **7750 angstroms**.