What are matter waves ? Find the ratio of de Broglie wavelengths associated with proton and alpha particles when both particles

(a) are accelerated through the same potential difference. (b) have same velocity.

 

 

 

 
 
 
 
 

Answers (1)

The de Broglie waves associated with moving particles are called matter waves

a) 

\lambda = \frac{h}{p}= \frac{h}{mv}= \frac{h}{\sqrt{2mE}}= \frac{h}{\sqrt{2mqV}}

\frac{\lambda_p}{\lambda_{\alpha}}=\sqrt{\frac{m\alpha q\alpha}{m_pq_p}}=\sqrt{\frac{4m_p 2q_p}{m_pq_p}}=2\sqrt{2}

b)

\\\frac{\lambda_p}{\lambda_{\alpha}}=\frac{m_{\alpha}}{m_p}(given\ v \ are\ same)\\\frac{\lambda_p}{\lambda_{\alpha}}=\frac{4}{1}

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