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De Broglie Wavelength Calculator
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If a particle of mass 'm' moving with a velocity 'v' having energy 'E' then it manifests itself in the form of a wave, its wavelength would be
$\lambda$ = $\frac{h}{p}$
where h = planck's constant and
p = momentum
This is de Broglie wave equation.
This wave will be having energy in terms of $\lambda$ as:
E = $\frac{hc}{\lambda}$
This is called De Broglie energy-wavelength relation.

De-Broglie wavelength calculator calculates energy and momentum of photon if wavelength is given and we can get the debroglie wavelength if energy or momentum is given.

## Steps for De Broglie Wavelength Calculator

Step 1 :

Analyze the problem. List out the given given quantities and find out which quantity is missing.

Step 2 :

If momentum of photon is given then use the formula

$\lambda$ = $\frac{h}{p}$

where h = Plancks constant,

p = momentum of photon.

If energy is given, then use formula

$\lambda$ = $\frac{h c}{E}$

Here E = Energy of Photon and

c = Velocity of light.

If Wavelength is given you can any of these formula and can get desired quantities of the two.

## Problems on De Broglie Wavelength Calculator

1. ### Calculate the de Broglie wavelength for an electron having velocity 5 $\times$ 105 m/s.If mass is 9.1 $\times$ 10-31 Kg.

Step 1 :

given: Mass m = 9.1 $\times$ 10-31 Kg,

Velocity V = 5 $\times$ 105 m/s,

Momentum of electron p = mv = 9.1 $\times$ 10-31 Kg $\times$ 5 $\times$ 105 m/s.

= 45.5 $\times$ 10-26 kgm/s.

Step 2 :

If momentum of photon is given then use the formula

$\lambda$ = $\frac{h}{p}$

= $\frac{6.624 \times 10^{-34}}{45.5 \times 10^{-26}}$

= 1.45 $\times$ 10-9 m.

$\lambda$ = 14.5 $A^{\circ}$

2. ### Calculate the momentum and energy for an electron if de-broglie wavelength is 0.24 $A^{\circ}$

Step 1 :

Mass m = 9.1 $\times$ 10-31 Kg,

Wavelength $\lambda$ = 0.24 $\times$ 10-10 m

Step 2 :

Using the formula

$\lambda$ = $\frac{h}{p}$

Then momentum is given by

p = $\frac{h}{\lambda}$

= $\frac{6.624 \times 10^{-34}}{0.24 \times 10^{-10}}$

= 2.76 $\times$ 10-26 kgm/s.

Energy is given by

E = $\frac{hc}{\lambda}$

= $\frac{6.624 \times 10^{-34} \times 3 \times 10^{8}}{0.24 \times 10^{-10}}$

= 8.28 $\times$ 10-15 eV.

Momentum p = 2.76 $\times$ 10-26 kgm/s.
Energy E = 8.28 $\times$ 10-15 ev.