SELECT * FROM question_mgmt as q WHERE id=2784 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=3 AND subId=8 AND chapterId=125 and ex_no='1' AND status=1 ORDER BY CAST(question_no AS UNSIGNED)

Question:

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which

(a) an electron, and

(b) a neutron, would have the same de Broglie wavelength.

Answer:

Wavelength of light of a sodium line, λ = 589 nm = 589 × 10−9 m

Mass of an electron, me= 9.1 × 10−31 kg

Mass of a neutron, mn= 1.66 × 10−27 kg

Planck’s constant, h = 6.6 × 10−34 Js

(a) For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation:

K = 1/2 mev2                                          ..... (1)

We have the relation for de Broglie wavelength as:

Substituting equation (2) in equation (1), we get the relation:

Hence, the kinetic energy of the electron is 6.9 × 10−25 J or 4.31 μeV.

 

(b) Using equation (3), we can write the relation for the kinetic energy of the neutron as:

Hence, the kinetic energy of the neutron is 3.78 × 10−28 J or 2.36 neV.


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