Work function a metal is `5.26 xx 10^(-18)` then its threshold wavelength will be :

Options

A. 736.7 Å
B. 760.7 Å
C. 301 Å
D. 376.4 Å

Explanation

To find the threshold wavelength of a metal given its work function, we can use the relationship between work function (φ), Planck's constant (h), speed of light (c), and wavelength (λ). The formula we will use is:

\[ \lambda_{threshold} = \frac{hc}{\phi} \]

### Step-by-Step Solution:

1. **Identify the Constants and Given Values**:
- Work function, φ = \(5.26 \times 10^{-18} \, \text{J}\)
- Planck's constant, h = \(6.626 \times 10^{-34} \, \text{J s}\)
- Speed of light, c = \(3.00 \times 10^{8} \, \text{m/s}\)

2. **Substitute the Values into the Formula**:
\[ \lambda_{threshold} = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{5.26 \times 10^{-18} \, \text{J}} \]

3. **Calculate the Numerator**:
\[ hc = 6.626 \times 10^{-34} \times 3.00 \times 10^{8} = 1.9878 \times 10^{-25} \, \text{J m} \]

4. **Calculate the Wavelength**:
\[ \lambda_{threshold} = \frac{1.9878 \times 10^{-25}}{5.26 \times 10^{-18}} \approx 3.77 \times 10^{-8} \, \text{m} \]

5. **Convert to Angstroms**:
Since \(1 \, \text{Å} = 10^{-10} \, \text{m}\),
\[ \lambda_{threshold} = 3.77 \times 10^{-8} \, \text{m} = 377 \, \text{Å} \]

6. **Final Result**:
The threshold wavelength is approximately \(376.4 \, \text{Å}\).