Question

The threshold wavelength of a metal is \(6000\ \text{\AA}\). The work function of the metal is (\(h = 6.62 \times 10^{-34}\ \text{J s}\))

• A. $3.31 \times 10^{19}$ J
• B. $3.31 \times 10^{-19}$ J
• C. $13.2 \times 10^{-19}$ J
• D. $13.2 \times 10^{19}$ J
• E. $1.5 \times 10^{-19}$ J

Hint:

For threshold wavelength: - $\phi = \frac{hc}{\lambda}$ - Always convert \AA{} to meters

Answer 1

The Correct Option is B

Concept: Work function: \[ \phi = \frac{hc}{\lambda} \]

Step 1: Convert wavelength.
\[ \lambda = 6000\ \text{\AA} = 6000 \times 10^{-10} = 6 \times 10^{-7}\ \text{m} \]

Step 2: Substitute values.
\[ \phi = \frac{6.62 \times 10^{-34} \times 3 \times 10^8}{6 \times 10^{-7}} \]

Step 3: Simplify.
\[ \phi = \frac{19.86 \times 10^{-26}}{6 \times 10^{-7}} = 3.31 \times 10^{-19}\ \text{J} \]