Question

Calculate(a)wave number and(b)frequency of radiation having wave length 2000A°​

Answer 1

ANSWER:

• (a) Wave number = 3.14 × 10⁷ m⁻¹.

• (b) Frequency = 1.5 × 10¹⁵ s⁻¹.

GIVEN:

• Wave length 2000 A°.

TO FIND:

• (a) Wave number.

• (b) Frequency.

EXPLANATION:

$\boxed{ \large{ \bold{ \gray{Wave \ number(k) = \dfrac{2\pi}{\lambda}}}}}$

$\sf \lambda = 2000 \ A^{\circ}$

$\boxed{ \large{ \bold{ \gray{1 \ A^{\circ} = {10}^{ - 10} \ m}}}}$

$\sf \lambda = 2000 \times {10}^{ - 10} \ m$

$\sf \lambda = 2 \times {10}^{ - 7} \ m$

$\sf k =\dfrac{2\pi}{2\times10^{-7}}$

$\sf k =\dfrac{3.14}{10^{-7}}$

$\sf k =3.14 \times 10^{7} \ {m}^{ - 1}$

$\boxed{ \large{ \bold{ \gray{Frequency( \nu) = \dfrac{c}{\lambda}}}}}$

$\sf \nu = \dfrac{3 \times {10}^{8} }{2\times 10^{-7}}$

$\sf \nu = \dfrac{1.5 \times {10}^{8} }{ 10^{-7}}$

$\sf \nu = 1.5 \times 10^{15}$

$\sf \nu = 1.5 \times 10^{15} \ {s}^{ - 1}$

$\ {\sf \therefore Wave \ number =3.14 \times 10^{7} \ {m}^{ - 1}}$

$\ \sf \therefore Frequency = 1.5 \times 10^{15} \ {s}^{ - 1}$

EXTRA POINTS:

• Some times, wave number is also defined as reciprocal of wavelength.

$\boxed{ \large{ \bold{ \gray{Wave \ number(k) = \dfrac{1}{\lambda}}}}}$

$\sf \lambda = 2000 \ A^{\circ}$

$\boxed{ \large{ \bold{ \gray{1 \ A^{\circ} = {10}^{ - 10} \ m}}}}$

$\sf \lambda = 2000 \times {10}^{ - 10} \ m$

$\sf \lambda = 2 \times {10}^{ - 7} \ m$

$\sf k =\dfrac{1}{2\times10^{-7}}$

$\sf k =\dfrac{0.5}{10^{-7}}$

$\sf k =0.5 \times 10^{7} \ {m}^{ - 1}$

$\sf k =5 \times 10^{6} \ {m}^{ - 1}$

Hence wavenumber can be 5 × 10⁶ m⁻¹, if we cosider the above formula.