Question 130: Dual Nature of Matter and Radiation

Question

A free electron of 2.6 eV energy collides with a H
+
ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $$	imes$$ 10
$$-$$34
Js)

Accepted Answer

For every large distance P.E. = 0
& total energy = 2.6 + 0 = 2.6 eV
Finally in first excited state of H atom total energy = $$-$$3.4 eV
Loss in total energy = 2.6 $$-$$ ($$-$$3.4) = 6 eV
It is emitted as photon
$$\lambda  = {{1240} \over 6} = 206$$ nm
$$f = {{3 	imes {{10}^8}} \over {206 	imes {{10}^{ - 9}}}}$$ = 1.45 $$	imes$$ 10
15
Hz
= 1.45 $$	imes$$ 10
9
Hz

Answer

1.45 $$	imes$$ 10
16
MHz

Answer

0.19 $$	imes$$ 10
15
MHz

Answer

1.45 $$	imes$$ 10
9
MHz

Answer

9.0 $$	imes$$ 10
27
MHz

Dual Nature of Matter and Radiation

A free electron of 2.6 eV energy collides with a H + ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 $\times 10 -$34 Js)

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