3. The nuclear potential that binds protons and neutrons in the nucleus of an atom
is often approximated by a square well. Imagine a proton confined in an infinite
square well of length 10−5 nm, a typical nuclear diameter. Calculate the wavelength
and energy associated with the photon that is emitted when the proton undergoes a
transition from the first excited state (n = 2) to the ground state (n = 1). In what
region of the electromagnetic spectrum does this wavelength belong?
Answer 3
We are given that,
Length of square well = L = 10−5
nm = 10−14 m.
Energy of proton in state n is given by,
En =
π
2n
2~
2
2mpL2
,
where L is the width of the square well.
⇒ E1 =
π
2~
2
2mpL2
E2 =
4π
2~
2
2mpL2
·
Explanation:
Simple Machine: Any of various devices that function in a manner basic to any machine, such as a lever, pulley, wedge, screw, or inclined plane. Complex Machine: A device consisting of two or more simple machines working together. ... A wedge is driven or forced between objects to split, lift, or make them stronger.
Answer:
a) —0.5 j m/s
b) 4.5 i + 2.25 j m
Explanation:
<u>Givens:</u>
v_0 =3.00 i m/s
a= (-3 i — 1.400 j ) m/s^2
The maximum x coordinate is reached when dx/dt = 0 or v_x = 0 ,thus :
<em>v_x = v_0 + at = 0 </em>
(3.00 i m/s) + (-3 i m/s^2)t=0
t = (3 m/s)/-3 i m/s^2
t = -1 s
Therefore the particle reaches the maximum x-coordinate at time t = 1 s.
Part a The velocity-of course- is all in the y-direction,therefore:
v_y =v_0+ at
We have that v_0 = 0 in the y-direction.
v_y = (-0.5 j m/s^2)(1 s)
= —0.5 j m/s
Part b: While the position of the particle at t = 1 s is given by:
r=r_0+v_0*t+1/2*a*t^2
Where r_0 = 0 since the particle started from the origin.
Its position at t = 1 s is then given by :
r =(3.00 i m/s)(1 s)+1/2(-3 i — 1.400 j )(1 s)^2
=4.5 i + 2.25 j m