Be sure to answer all parts. According to Einstein\'s special theory of relativi

Question

Be sure to answer all parts. According to Einstein's special theory of relativity, the mass of a moving particle, m moving, is related to its mass at rest, m rest, by the following equation m moving = m rest/squareroot 1 - (u/c)^2 where u and c are the speeds of the particle and light, respectively. In particle accelerators, protons, electrons, and other charged particle are often accelerated to speeds close to the speed of light. Calculate the wavelength (in nm) of a proton moving at 44.0 percent the speed of light. The mass of a proton id.673 x 10^-27 kg.

Explanation / Answer

here,

speed of particle , v = 0.44 c

mass of proton , mr = 1.673 * 10^-27 kg

mv = mr /( sqrt( 1- ( v/c)^2))

mv = 1.673 * 10^-27 /( sqrt( 1- ( 0.44 c/c)^2))

mv = 2.57 * 10^-27 kg

let the wavelength be lamda

E = mv * c^2 = h*c/lamda

2.57 * 10^-27 *3*10^8 = 6.62 * 10^-34 /lamda

lamda = 8.59 * 10^-16 m

lamda = 8.59 * 10^-7 nm

the wavelength of proton is 8.59 * 10^-7 nm

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