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Chapter 28: Q31P (page 831)

A particular type of fundamental particle decays by transforming into an electron e鈭�and a positron e+. Suppose the decaying particle is at rest in a uniform magnetic field of magnitude3.53mT and the e鈭� and e+move away from the decay point in paths lying in a plane perpendicular to B鈫� . How long after the decay do the e鈭� and e+collide?

Short Answer

Expert verified

e鈭�and e+ will collide after 5.05脳10鈭�9鈥�s following the decay.

Step by step solution

01

Listing the given quantities

Magnetic field B=3.53鈥�mT=3.53脳10鈭�3鈥�T.

02

Understanding the concept of the period of motion

We need to use the formula of the period of motion of charged particle into a magnetic field to find the period of the particle. As each particle travels only a half-circular path, dividing this period by 2, we will get the required time after which andwill collide.

Formula:

T=2蟺me/qB

03

Calculation of theafter the decay when  e-and e+  collide

We have:

T=2蟺meqB=2蟺(9.1脳10鈭�31鈥塳驳)(1.6脳10鈭�19鈥塁)(3.53脳10鈭�3鈥涂)=1.01脳10鈭�8鈥塻

But, each particle travels only a half-circular path. So,

t=T2=1.01脳10鈭�8鈥�s2=5.05脳10鈭�9鈥�s

Therefore, 5.05脳10鈭�9鈥�safter of the decay, e鈭�and e+will collide.

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Most popular questions from this chapter

An electron that has velocity 谓鈫�=(2.0脳106m/s)i^+ (3.0脳106m/s)moves through the uniform magnetic field B鈫�= (0.030T)i^-(0.15T)j^.(a)Find the force on the electron due to the magnetic field. (b)Repeat your calculation for a proton having the same velocity.

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