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Q 13CQ

Expert-verifiedFound in: Page 186

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?**

**Answer:**

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

**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**

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

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.

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