The wave function of a metal is 8.0 x \(10^{-19}\)J. Calculate the wavelength of its...

WAEC 1994

The wave function of a metal is 8.0 x \(10^{-19}\)J. Calculate the wavelength of its threshold frequency. (Speed of light in a vacuum = 3 x \(10^8ms^{-1}, Planck's constant = 6.6 \times 10^{-34}\)Js)

A. 0.8 x \(10^{-7}\)m
B. 1 x \(10^{-7}\)m
C. 2.3 x \(10^{-7}\)m
D. 3.8 x \(10^{-7}\)m
E. 12.4 x \(10^{-7}\)m

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Correct Answer: Option C

Explanation

\(\theta = E - E_f = h_f = \frac{v}{\lambda} \Rightarrow = \lambda = \frac{h_v}{\theta}
\frac{6.6\times 10^{-34} \times 3 \times 10^{8}}{8.6 \times 10^{-19}} = 0.8 \times 10^{-7}\)m

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