Question 187: Dual Nature of Matter and Radiation

Question

A particle is moving 5 times as fast as an
electron. The ratio of the de-Broglie wavelength
of the particle to that of the electron is 1.878 $$ 	imes $$
10–4. The mass of the particle is close to

Accepted Answer

Let mass of particle = m
Let speed of e
Ã¢ÂÂ
= V
$$ 	herefore $$ speed of particle = 5V
de-broglie wavelength $$\lambda $$
d
= $${h \over P} = {h \over {mv}}$$
$$ 	herefore $$ ($$\lambda $$
d
)
P
= $${h \over {m\left( {5V} ight)}}$$ ....(1)
and ($$\lambda $$
d
)
e
= $${h \over {{m_e}\left( V ight)}}$$ ....(1)
According to question
$${{{{\left( {{\lambda _d}} ight)}_P}} \over {{{\left( {{\lambda _d}} ight)}_e}}} = {{{m_e}} \over {5m}}$$ = 1.878 $$ 	imes $$
10
Ã¢ÂÂ4
$$ \Rightarrow $$ m = $${{{m_e}} \over {5 	imes 1.874 	imes {{10}^{ - 4}}}}$$
= $${{9.1 	imes {{10}^{ - 31}}} \over {5 	imes 1.874 	imes {{10}^{ - 4}}}}$$
= 9.7 $$ 	imes $$ 10
Ã¢ÂÂ28
kg

Answer

1.2 $$ 	imes $$ 10–28 kg

Answer

9.1 $$ 	imes $$ 10–31 kg

Answer

4.8 $$ 	imes $$ 10–27 kg

Answer

9.7 $$ 	imes $$ 10–28 kg

Dual Nature of Matter and Radiation

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $ \times $ 10–4. The mass of the particle is close to

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