Question

Calculate Frequency, Wavelength and wave number of the photon with energy $\sf 5.68\times 10^{-14}J$.

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Answer 1

Answer:

Given,

Energy, E = $\sf 5.68\times 10^{-14}J$.

To find :

1) Frequency, f =?

2) Wavelength, $\lambda$ =?

3) wave number, n =?

We know that,

plunk constant $\:h\:=\:6.626\times 10^{-34}\:\:Js$

velocity of light / photon , c = $\sf 3\times 10^{8}\:\:ms^{-1}$.

Solution :

1)

$\sf \: we \: know \: that \: \\ \: \: \: \: \: \: \: \bf \: E = hf \\ \implies \: f \: = \frac{E }{ h} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf \frac{5.68 \times {10}^{ - 14} }{6.626 \times {10}^{ - 34} } \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8.57 \times {10}^{19} \: \: Hz \: \\ \boxed{\green{\sf \therefore \:frequency \: f = 8.57 \times {10}^{19} \: \: Hz}}$

2)

$\sf \: we \: know \: that \: \\ \sf \: c = f \lambda \\ \implies \sf \lambda = \frac{c}{f} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3 \times {10}^{8} }{8.57 \times {10}^{19} } \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.5 \times {10}^{ - 12} \: \: m \\ \\ \boxed{ \green{{ \sf \therefore\: wavelength \: \lambda = 3.5 \times {10}^{ - 12} }}}$

3)

$\sf \: we \: know \: that \: \\ \sf \: wave \: number \: \: \: \: n \: = \frac{1}{ \lambda} \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3.5 \times {10}^{ - 12} } \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: = 2.8 \times {10}^{11} \: \: {m}^{ - 1} \\ \\ \boxed{ \green {\sf \therefore\:wave \: number \: \: n \: = 2.8 \times {10}^{11 } \: \: {m}^{ - 1} }}$

Answer 2

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If you use Planck-Einstein equation,

E = h.f where h is Planck's constant,

which 6.626 x 10^−34 J.s, then you can work out the frequency:

f = E/h

=5.68 x 10^-14/6.626 x 10−34

=0.85×10^20

 Then convert frequency to wavelength using λ = c/f where c is the speed of light, 3 x 10^8 m/sec.

λ = 3 x 10^8 / 0.85×10^20

=3.529×10^-12