First slide

Electromagnetic radiation and spectra

Question

wavelength of 400 nm corresponds to

Moderate

A

$frequency (v) = 7 .5 \times 10^{14} Hz$
B

$wave number (\bar{v}) = 2 .5 \times 10^{6} m^{- 1}$
C

$momentum (mv) = 1 .66 \times 10^{- 27} kg {ms}^{- 1}$
D

All of the above

Solution

$(d) Wavelength, λ = 400 nm = 400 \times 10^{- 9} m$
$(a) Frequency, v = \frac{c}{λ} = \frac{3 \times 10^{8} {ms}^{- 1}}{400 \times 10^{- 9} m} = 7.5 \times 10^{14} s^{- 1}$
$= 7.5 \times 10^{14} Hz (correct)$
$(b) \frac{1}{λ} = \bar{v} (wave number)$
$= \frac{1}{400 \times 10^{- 9}} = 2 .5 \times 10^{6} m^{- 1} (correct)$
$(c) λ = \frac{h}{p} = \frac{h}{mv}$
$\begin{matrix} ∴ Momentum, mv = \frac{h}{λ} = \frac{6 .62 \times 10^{- 34} Js}{400 \times 10^{- 9} m} \\ = 1 .66 \times 10^{- 27} J {sm}^{- 1} \\ = 1 .66 \times 10^{- 27} {kgm}^{2} s^{- 2} m^{- 1} s [1 J = 1 {kgm}^{2} s^{- 2}] \\ = 1 .66 \times 10^{- 27} kg {ms}^{- 1} (correct) \end{matrix}$

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