Question 166: 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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