The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2 E$ , is $n : 1$ . The value of $n$ is $____$ .
(Assume mass of proton $=$ mass of neutron):

Question

The ratio of de Broglie wavelength of a deutron with kinetic energy

E

to that of an alpha particle with kinetic energy

2 E

, is

n : 1

. The value of

n

is

____

.
(Assume mass of proton

=

mass of neutron):

Accepted Answer

Correct answer: 2. (2) The de Broglie wavelength is = h 2 mE. For a deuteron (mass m_d=2m_p ) with energy E : _d= h 2 2m_p E= h 4m_pE For an alpha particle (mass m_ =4m_p ) with energy 2E : _ = h 2 4m_p 2E= h 16m_pE The ratio: _d _ = 16m_pE 4m_pE= 4=2

$The ratio of de Broglie wavelength of a deutron with kinetic energy E to that of an alpha particle with kinetic energy 2 E, is n : 1 . The value of n is____. (Assume mass of proton = mass of neutron):$

Solution

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