$module$/Default for Homework 9 due 10//6
matching speed in H
Free electrons are most easily captured into an atomic orbit when their kinetic energy matches the kinetic energy associated with that orbit. What is the speed in m/s that a free electron should have to facilitate its capture into the Bohr orbit for n={n} in a completely ionized nucleus with Z={Z}?
1
0.1
0
0
3e8*{Z}/{n}*sqrt(2*13.6/511000)
0.005
1
2
3
private
Z
calculated
uniform
2
20
0
40
1
4
2
9
3
4
4
17
5
3
6
5
7
16
8
5
9
13
10
18
11
8
12
3
13
18
14
10
15
5
16
7
17
19
18
3
19
16
20
18
21
15
22
6
23
14
24
6
25
8
26
14
27
2
28
14
29
11
30
12
31
8
32
18
33
9
34
18
35
13
36
19
37
13
38
10
39
8
40
16
40
private
n
calculated
uniform
2
20
0
40
1
7
2
9
3
18
4
18
5
18
6
17
7
12
8
7
9
6
10
11
11
16
12
2
13
3
14
11
15
12
16
18
17
7
18
13
19
4
20
12
21
8
22
11
23
6
24
20
25
4
26
8
27
15
28
19
29
19
30
4
31
15
32
15
33
10
34
12
35
17
36
5
37
17
38
11
39
14
40
10
40
photo-ionized hydrogen
Suppose a hydrogen atom in the ground state absorbs a photon of wavelength {lambda} nm. What will be the kinetic energy of the emitted electron when it gets far away from its atom of origin?
1
0.1
0
0
1240/{lambda}-13.6
0.005
1
2
3
private
lambda
calculated
uniform
10
60
1
40
1
59.3
2
21.6
3
57.1
4
21.5
5
52.5
6
25.7
7
40.7
8
39.6
9
19.1
10
11.9
11
58.5
12
40.3
13
12.0
14
43.3
15
58.0
16
33.1
17
41.9
18
20.0
19
14.1
20
18.1
21
36.6
22
24.4
23
16.7
24
52.9
25
10.1
26
38.7
27
36.9
28
43.4
29
56.2
30
47.7
31
37.3
32
22.1
33
28.9
34
46.3
35
24.8
36
55.9
37
20.5
38
23.4
39
19.8
40
19.0
40
Rydberg wavelength
Find the wavelength in nm for transitions from the n={n} to the n={np} state for an ion with a single electron with Z={Z}.
1
0.1
0
0
1/({Z}*{Z}*0.0109747*(1/({np}*{np})-1/({n}*{n})))
0.005
1
2
3
private
Z
calculated
uniform
5
25
0
41
1
5
2
15
3
11
4
8
5
16
6
8
7
20
8
21
9
12
10
11
11
11
12
8
13
25
14
6
15
5
16
13
17
11
18
19
19
18
20
12
21
22
22
17
23
6
24
21
25
19
26
7
27
17
28
8
29
19
30
19
31
18
32
20
33
15
34
22
35
10
36
12
37
6
38
8
39
20
40
10
41
7
41
private
np
calculated
uniform
2
5
0
41
1
3
2
3
3
4
4
4
5
2
6
4
7
5
8
3
9
3
10
5
11
4
12
2
13
3
14
4
15
3
16
3
17
4
18
3
19
2
20
4
21
3
22
5
23
2
24
5
25
4
26
5
27
4
28
4
29
4
30
5
31
5
32
3
33
2
34
4
35
2
36
3
37
2
38
3
39
3
40
3
41
3
41
private
n
calculated
uniform
6
12
0
41
1
12
2
9
3
7
4
8
5
10
6
8
7
9
8
11
9
11
10
10
11
6
12
6
13
8
14
7
15
11
16
11
17
7
18
10
19
10
20
10
21
6
22
10
23
7
24
6
25
12
26
8
27
11
28
7
29
11
30
8
31
10
32
12
33
8
34
12
35
7
36
6
37
11
38
6
39
11
40
7
41
8
41
ionized hot hydrogen
Using the fact that the average energy of a gas atom is 3/2 kT, estimate the minimum temperature of a gas of atomic hydrogen that will produce appreciable ionization of the atoms through collisions so that the hydrogen atoms will be broken up into protons and electrons (a plasma). [This question has no online answer.]
1
0
0
0
positronium
Calculate the ground state energy of positronium. Positronium is a hydrogen-like “atom,” but consisting of an electron and a positron rather than an electron and a proton. A positron has the same charge as a proton but the same mass as an electron (it is the anti-matter equivalent of an electron). [No online answer for this question.]
1
0
0
0