Electron spin: Radio astronomers can detect clouds of hydrogen too cool to radiate optical wavelengths of light by means of the
1 answer:
Answer:
the magnetic field experienced by the electron is 0.0511 T
Explanation:
Given the data in the question;
Wavelength λ = 21 cm = 0.21 m
we know that Bohr magneton μ is 9.27 × 10⁻²⁴ J/T
Plank's constant h is 6.626 × 10⁻³⁴ J.s
speed of light c = 3 × 10⁸ m/s
protein spin causes magnetic field in hydrogen atom.
so
Initial potential energy = -μB × cos0°
= -μB × 1
= -μB
Final potential energy = -μB × cos180°
= -μB × -1
= μB
so change in energy will be;
ΔE = μB - ( -μ
B )
ΔE = 2μB
now, difference in energy levels will be;
ΔE = hc/λ
2μB = hc/λ
2μBλ = hc
B = hc / 2μλ
so we substitute
B = [(6.626 × 10⁻³⁴) × (3 × 10⁸)] / [2(9.27 × 10⁻²⁴) × 0.21 ]
B = [ 1.9878 × 10⁻²⁵ ] / [ 3.8934 × 10⁻²⁴ ]
B = 510556326.09
B = 0.0511 T
Therefore, the magnetic field experienced by the electron is 0.0511 T
You might be interested in
4. The Coyote has an initial position vector of .
4a. The Coyote has an initial velocity vector of . His position at time
is given by the vector
where is the Coyote's acceleration vector at time
. He experiences acceleration only in the downward direction because of gravity, and in particular
where
. Splitting up the position vector into components, we have
with
The Coyote hits the ground when :
4b. Here we evaluate at the time found in (4a).
5. The shell has initial position vector , and we're told that after some time the bullet (now separated from the shell) has a position of
.
5a. The vertical component of the shell's position vector is
We find the shell hits the ground at
5b. The horizontal component of the bullet's position vector is
where is the muzzle velocity of the bullet. It traveled 3500 m in the time it took the shell to fall to the ground, so we can solve for
:
A) Vector A
The x-component of a vector can be found by using the formula
where
v is the magnitude of the vector
is the angle between the x-axis and the direction of the vector
- Vector A has a magnitude of 50 units along the positive x-direction, so . So its x-component is
- Vector B has a magnitude of 120 units and the direction is (negative since it is below the x-axis), so the x-component is
So, vector A has the greater x component.
B) Vector B
Instead, the y-component of a vector can be found by using the formula
Here we have
- Vector B has a magnitude of 50 units along the positive x-direction, so . So its y-component is
- Vector B has a magnitude of 120 units and the direction is , so the y-component is
where the negative sign means the direction is along negative y:
So, vector B has the greater y component.