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Chapter 6: Q20E (page 1314)

A hydrogen atom initially in its ground level absorbs a photon, which excites the atom to the n=3 level. Determine the wavelength and frequency of the photon.

Short Answer

Expert verified

The wavelength and frequency of the photon are1.02脳10-7mand 2.92脳1015Hzrespectively.

Step by step solution

01

Define the energy.

The energy Eof a photon is inversely proportional to the wavelength 位of photon and directly proportional to the frequency fof wave

E=hfE=hc位

Where, the value of Planck鈥檚 constant h=6.26脳10-34J.s.

In the Bohr model for the hydrogen atom the equations energyEn of the nthorbit is:

En=-13.50eVn2

02

Determine the wavelength and frequency of the photon.

The energy of the ground level is:

E=-13.61.0=13.60eV

The energy of the n=3level is:

E3=-13.603.02=-1.51ev

The frequency of the photon is:

f=E2-E1h=-1.51--13.604.136x10-15=2.92x1015Hz

The wavelength of the photon is:

位=cf=3x1062.92x1015=1.02x107m

Hence, the wavelength and frequency of the photon are 1.02x107and2.92x1015Hz respectively.

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