If the threshold wavelength for a certain metal is `2000Å`, then the work function of the metal is

Options

A. `6.2`J
B. `6.2eV`
C. `6.2MeV`
D. `6.2Ev`

Answer

To find the work function of a metal given its threshold wavelength, we can use the formula that relates energy to wavelength. The work function (φ) can be calculated using the equation:

\[ E = \frac{hc}{\lambda} \]

where:
- \( E \) is the energy (in electron volts),
- \( h \) is Planck's constant (\( 4.1357 \times 10^{-15} \) eV·s),
- \( c \) is the speed of light (\( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength (in meters).

Given that the threshold wavelength \( \lambda \) is \( 2000 \) Å (angstroms), we first convert this to meters:

1. **Convert the wavelength from angstroms to meters**:
\[ 2000 \, \text{Å} = 2000 \times 10^{-10} \, \text{m} = 2 \times 10^{-7} \, \text{m} \]

2. **Use the formula to calculate the energy**:
\[ E = \frac{hc}{\lambda} \]
Plugging in the values:
\[ E = \frac{(4.1357 \times 10^{-15} \, \text{eV·s})(3 \times 10^8 \, \text{m/s})}{2 \times 10^{-10} \, \text{m}} \]

3. **Calculate the energy**:
\[ E = \frac{(4.1357 \times 3) \times 10^{-7}}{2} \, \text{eV} \]
\[ E = \frac{12.4071 \times 10^{-7}}{2} \, \text{eV} = 6.20355 \, \text{eV} \]

4. **Round to appropriate significant figures**:
The energy can be rounded to \( 6.2 \, \text{eV} \).

Thus, the work function \( \phi \) of the metal is \( 6.2 \, \text{eV} \).

### Final Answer:
The work function of the metal is \( 6.2 \, \text{eV} \).

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