Question

calcute the frequency, wave number of an electro magnetic whoes wave length is 2000A in cm​

Answer 1

Given :

•Wavelength =2000A

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To Find :

• Frequency =?

• wave number =?

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Formula :

$\blue \bigstar \boxed{ \sf{wave \: number \: = \frac{1}{ \lambda}}}$

$\\ \blue \bigstar \boxed{ \sf{velocity = frequency \times \lambda}}$

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Solution :

➡$\rm{2000A=2000 \times 10^{-10}m}$

$\\ \implies \sf \: wave \: number \: = \frac{1}{ \lambda} \\ \\ \implies \sf \: wave \: number = \frac{1}{2000 \times {10}^{ - 10} } \\ \\ \implies \sf \: wave \: number = \frac{1}{2 \times {10}^{3} \times {10}^{ - 10} } \\ \\ \implies \sf \: wave \: number = \frac{1}{2 \times {10}^{ - 7} } \\ \\ \implies \sf \: wave \: number = \frac{ {10}^{7} }{2} \\ \\ \implies \sf \: wave \: number = \frac{ \cancel{10 }\times {10}^{6} }{ \cancel2} \\ \\ \implies \sf \: wave \: number \: = 5 \times {10}^{6} \\ \\ \implies \boxed{ \sf{wave \: number \: = 5 \times {10}^{6} {m}^{ - 1} }}$

hence wave number is $\rm{5 \times 10^{6}m^{-1}}$

For finding frequency we use second formula :

$\\ \quad \implies \sf \: \lambda = \frac{v}{f} \\ \\ \quad\implies \bf{ \underline{v (speed \: of \: light) = 3 \times {10}^{8} }} \\ \\ \\ \quad\implies \sf \: f = \frac{v}{ \lambda} \\ \\ \quad \implies \sf \: frequency = \frac{3 \times {10}^{8} }{2000 \times {10}^{ - 10} } \\ \\ \quad \implies \sf \: frequency = \frac{3 \times {10}^{8} }{2 \times {10}^{ - 7} } \\ \\ \quad\implies \sf \: frequency = \frac{3 \times {10}^{8 + 7} }{2} \\ \\ \quad \implies \sf \: frequency = \frac{30 \times {10}^{14} }{2} \\ \\ \quad \implies \sf \: frequency = 15 \times {10}^{14} hertz \\ \\ \quad \implies \boxed{ \sf{frequency = 15 \times {10}^{14} \: hertz}}$

Hence Frequency =$\rm{15\times 10^{14} \:Hertz}$