A proton and an alpha particle are accelerated from rest by different potential differences such that their final de Broglie wavelengths are identical. If the ratio of the accelerating potential of the proton to that of the alpha particle i

Question

A proton and an alpha particle are accelerated from rest by different potential differences such that their final de Broglie wavelengths are identical. If the ratio of the accelerating potential of the proton to that of the alpha particle is x , then the value of x is _ _ _ _ _ .

Quantrex Academy · Accepted Answer

Correct answer: 8

The de Broglie wavelength of a charged particle accelerated through a potential difference V is given by = h 2mqV . Given that _p = _ , we have: h 2m_p q_p V_p = h 2m_ q_ V_ Squaring both sides and rearranging gives: m_p q_p V_p = m_ q_ V_ For a proton, let mass m_p = m and charge q_p = e . For an alpha particle, mass m_ = 4m and charge q_ = 2e . Substituting these values: (m)(e)V_p = (4m)(2e)V_ V_p = 8 V_ The ratio V_p V_ = 8 . Answer: 8

A proton and an alpha particle are accelerated from rest by different potential differences such that their final de Broglie wavelengths are identical. If the ratio of the accelerating potential of the proton to that of the alpha particle is x , then the value of x is _ _ _ _ _ .

Correct answer

Step-by-step solution

More from Structure of Atom