Physic 1). A proton is released by a particle accelerator. At what speed will th

Question

Physic

1). A proton is released by a particle accelerator. At what speed will the proton move in the magnetic field so as to increase its mass to 6 times its rest mass ?

2) . A slit is illuminated by lights with two different wavelengths. One wavelength is 6,000 nm. On a screen, the third dark fringe of the interference pattern for the 6,000 nm wavelength coincides with the fifth bright fringe for the other wavelength. What is the unknown wavelength ? (fringes are counted from the central bright fringe. )

Explanation / Answer

relastivistic mass m = m0/sqrt(1-(v/c)^2)

m0 = rest mass

m = 6*m0

6*m0 = m0/sqrt(1-(v/c)^2)

6 = 1/sqrt(1-(v/c)^2)

6 = 1/sqrt(1-(v)^2)

speed of proton v = 0.98c

===============================

(2)

for lambda 1 = 6000*10^-9 m

y3 = 5*lambda*R/(2d)

for lambda 2 = ?

y5 = 5*lambda2*R/d

y3 = y5

(5/2)*lambda1 = 5*lambda2

(5/2)*6000*10^-9 = 5*lambda2

lambda2 = 3000 nm <<<-----answer

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