A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813 * 10^{-4} . Calculate the particle’s mass and identify the particle.

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De Broglie's Matter Waves – University Physics Volume 3
Today, this idea is known as de Broglie's hypothesis of matter waves. In 1926, De Broglie's hypothesis, together with Bohr's early quantum theory, ... Any particle that has energy and momentum is a de Broglie wave of frequency f and wavelength \lambda : ... For matter waves, this group velocity is the velocity u of the particle.
For more information, see De Broglie's Matter Waves – University Physics Volume 3
Recall the de Broglie wavelength formula
de Broglie wavelength \lambda = \frac{h}{p}
Where, h - Planck constant = 6.63* 10^{-34} J and p - linear momentum
Given that
A particle is moving = 3 * electron speed
v = 3 * v_e
\frac{v}{v_e} = 3 .............................(1)
Ratio of de Broglie Wavelength of the particle to the electron
\frac{\lambda_{\text{ partical }}}{\lambda _{\text{ electron }}} = \frac{\lambda }{\lambda_e} = 1.813*10^{-4}
Mass of an electron m_e = 9.11 × 10^{-31} kilograms
For a moving particle
mass - m
speed - v
de Broglie wavelength \lambda = \frac{h}{p} = \frac{h}{mv}
Mass m = \frac{h}{\lambda v}
m = \frac{h}{\lambda 3v_e} ...............................(2) \because eq(1)
For an electron
mass - m_e
speed - v_e
de Broglie wavelength \lambda_e = \frac{h}{m_e v_e}
Mass m_e = \frac{h}{\lambda_e v_e} .............................(3)
Dividing equation (32) by equation (21)
\frac{eq(3)}{eq(2)}
\frac{m}{m_e}=\frac{\frac{h}{\lambda3v_e}}{\frac{h}{\lambda_ev_e}}
\frac{m}{m_e} = \frac{h}{\lambda (3 v_e)} * \frac{\lambda_e v_e}{h}
\frac{m}{m_e} = \frac{1}{3}* \frac{\lambda_e}{\lambda}
\frac{m}{m_e} = \frac{1}{3} * \frac{1}{1.813*10^{- 4}}
m = m_e * \frac{1}{3} * \frac{1}{1.813*10^{- 4}}
m = (9.11*10^{-31} kg) * \frac{1}{3} * \frac{1}{1.813*10^{- 4}}
m = 1.675 *10^{-27} kg
Hence, the particle may be a proton or a neutron with this mass