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  • The de Broglie wavelength of a proton and - particle are equal. The ratio of their velocities is :   Option: 1 4:1 Opti

The de Broglie wavelength of a proton and \alpha - particle are equal. The ratio of their velocities is :
 
Option: 1 4:1
Option: 2 4:2
Option: 3 1:4  
Option: 4 4:3

Answers (1)

best_answer

The de-Broglie equation is given by:
\lambda=\frac{h}{m v}

So, If the de-Broglie wavelength for both the proton and alpha particle is the same then
\\ \Rightarrow \lambda_{1}=\lambda_{2} \\ \Rightarrow\left(\frac{h}{m_{1} v_{1}}\right)=\left(\frac{h}{m_{2} v_{2}}\right)

And using m_2=4m_1

m_{1} v_{1}=m_{2} v_{2} \\ \Rightarrow m_{1} v_{1}=4 m_{1} v_{2} \\ \Rightarrow v_{1}=4 v_{2} \\ \therefore \frac{v_{1}}{v_{2}}=\frac{4}{1}

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avinash.dongre

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