homework help please! An electron gun works as follows: A filament of metal (cal

Question

homework help please!

An electron gun works as follows: A filament of metal (called a cathode) is heated so that it emits electrons in what's known as thermionic radiation. A potential difference V_1 is applied across the cathode and an anode some distance d_1 away, which accelerates the electrons towards the anode. There's a small hole in the anode through which the electrons are emitted as a collimated beam, which for our purposes can be considered to be, at the moment it is emitted from the anode, perfectly straight and oriented horizontal to the surface of the earth. Immediately upon emission the electrons are acted upon by earth's gravity, which wants to pull them downward according to their weight with a force of magnitude F_w = m_eg. At the same time, the electron beam flies immediately into the space between a pair of parallel plates some distance d_2 apart. These plates have some length L. If the voltage V_1 is not high enough, the electrons will not have enough kinetic energy to fly all the way through the plates. When a potential difference V_2 is applied across the plates, this helps to balance out the force due to gravity and allow the electrons to keep flying. (a) What is the charge-to-mass ratio of the electron? (b) Assume that V_2 is 0. How long does it take the electrons to hit the bottom plate if the distance between them d_2 = 01 m? (c) If the length of the plates is 1 m, what velocity is necessary for the electrons to hit the plate half way down its length? (d) If the distance between the cathode and the anode d_1 = 005 m, what voltage V_1 is necessary to accelerate the electrons so that they hit the plate half way down its length? (e) Given the information from a) and b), what voltage V_2 is necessary to allow the electrons to fly straight through without being deflected up or down? Does this answer depend upon V_1? (f) What is the work done on the electrons as they move across the parallel plates?

Explanation / Answer

a. charge of an electron = 1.6 x 10-19 C

mass of an electron = 9.1 x 10-31 kg

charge -to- mass ratio = 1.6 x 10-19 / 9.1 x 10-31 = 0.176 x 1012 : 1

b. For this motion

initial velocity = u =0

acceleration = a = g=9.8 m/s2

distance covered= s= 0.01 m

applying equation of motion

s= ut + 1/2 x a x t2

so, 0.01 =0 +0.5 x 9.8 x t2

so t= 0.045 s

so time taken will be 0.045 s

c. length of paltes = l=0.1m

so, distance to cover= half the length of plate =0.1/2=0.05 m

so velocity = distance/time = 0.05/0.045 = 1.11 m/s

necessary velocity=1.11 m/s

d. If d1=0.005 m

then final velocity for this journey = v= 1.11 m/s

initial velocity = u= 0

acceleration =?

applying equation of motion

v2 - u2 =2as

so, 1.112 = 2 x a x 0.005

so, a= acceleration during this journey = 123.21 m/s2

acceleration = charge x Potential difference/( distance x mass)

so, 123.21 = 1.6 x 10-19 x potential difference/(0.005 x 9.1 x 10-31)

so, potential difference = 3.5 x 10-12 V

potential difference necessary is 3.5 x 10-12 V

ALL THE BEST IN THE COURSE WORK

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.