CBSE Class 12 Physics 2015 Delhi Set 1 Paper

Question : 6 of 26

Marks: +1, -0

SECTION - B

A proton and an

α

-particle have the same deBroglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds.

Solution:

Ans. Determination of ratio (i) accelerating potential
(ii) speed
(i)

λ\;=\;{h}/{{√{2 m q V}}}

V\;=\;{h^2}/{2 m q λ^2}

m_α\;=4 m_p q_α=2 q_p

⇒ \;\; \;{V_p}/{V_α}\;=\;{m_α q_α}/{m_p q_p}

\;=\;{4 m_p × 2 q_p}/{m_p q_p}

\;=8: 1

(ii)

λ\;=\;{h}/{m v}

⇒ v\;=\;{h}/{m λ}

⇒ \;{v_p}/{v_α}\;=\;{m_α}/{m_p}=4

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