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Q 13CQ

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Found in: Page 186

### Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

# In the harmonic oscillators eave functions of figure there is variation in wavelength from the middle of the extremes of the classically allowed region, most noticeable in the higher-n functions. Why does it vary as it does?

There is a variation in wavelength from the middle to the extremes because of variation in kinetic energy and hence variation in momentum.

See the step by step solution

## Step 1: Wavelength

The wavelength gets longer near the extreme edges because the kinetic energy is low there.

As the Kinetic Energy is low, so the momentum is small. Because, we know that Kinetic energy is directly proportional to momentum by the following formula

$p=\sqrt{2m\left(KE\right)}$

## Step 2: Variations in Wavelengths

And we know that momentum is inversely proportional to wavelength by the formula

$\left(\lambda =\frac{h}{p}\right)$

So, a low kinetic energy corresponds to a longer wavelength.

Hence, Variation of wavelength from middle to extremes is seen because of variation in kinetic energy.