JEE MAIN - Physics (2021 - 18th March Morning Shift - No. 8)
A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :
$${1 \over {16}}$$ times the mass of e$$-$$
8 times the mass of e$$-$$
16 times the mass of e$$-$$
$${1 \over {8}}$$ times the mass of e$$-$$
Explanation
$$\lambda = {h \over p}$$
$${{{\lambda _p}} \over {{\lambda _e}}} = {{{p_e}} \over {{p_p}}} = {{{m_e}{v_e}} \over {{m_p}{v_p}}}$$
$$2 = {{{m_e}} \over {{m_p}}}\left( {{{{v_e}} \over {4{v_e}}}} \right)$$
$$ \therefore $$ $${m_p} = {{{m_e}} \over 8}$$
$${{{\lambda _p}} \over {{\lambda _e}}} = {{{p_e}} \over {{p_p}}} = {{{m_e}{v_e}} \over {{m_p}{v_p}}}$$
$$2 = {{{m_e}} \over {{m_p}}}\left( {{{{v_e}} \over {4{v_e}}}} \right)$$
$$ \therefore $$ $${m_p} = {{{m_e}} \over 8}$$
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