And his Atomic Theory

Niels Bohr was born on October 7, 1885 and he died on November 18, 1962. He was born in Copenhagen, Denmark and he died in the same area. His parents were Christian Bohr and Ellen Adler, (Bohr). He had an older sister named Jenny, who was born in 1883, and a younger brother named Harald who was born in 1887. Harald and Niels were very close through out his childhood and he was often heard saying that Harald was his best friend all through his life.

Niels entered the Grammelholms school in October of 1891, he attended this school for his complete secondary education. He did fairly well in school but could never lay claim to a brilliant mind, he usually came in forth or fifth in a class of twenty. In his last two years in school Niels specialized in mathematics and physics, he frightened his math teacher with his exceptional skills and would work ahead in the physics textbook often pointing out errors in the text. He was learned more about this subject than he did from his teachers.

Bohr entered the University of Copenhagen in 1903. Physics was his major and he had minors in mathematics and chemistry.

When he was in University he wouldn’t have been able to carry out any experiments in physics because the University didn’t have a laboratory, so he used his father’s physiology lab. And his first paper describes some of the experiments he did in the lab, he dedicated this paper to his brother, Harald. Due to this paper, Bohr, won the Gold Medal for 1906 from the Royal Danish Academy of Sciences, this was for his analysis of water jets being used to determine surface tension. He got his masters degree from the University of Copenhagen in 1909, and his doctorate in 1911for his thesis, Studies on the electron theory of metals. This thesis was dedicated to his father, who had died earlier in the year from a heart attack Bohr was engaged to Margrethe Norlund, who, many say, placed a key role in his successfulness, at the time of his father’s death.

In 1911 in the month of September Bohr went to England to study with J J Thompson at Cambridge, he had hoped to spend a long period of time with Thompson, but, unfortunately, they didn’t get along. Lucky for him, he had met Rutherford earlier in that year and went to study with him instead, this was right after Rutherford had published his theory, which states that the bulk of the mass of an atom can be found in the nucleus.

Bohr began developing his theory in June of 1912 He did his fundamental work on the hydrogen atom eventually he even did some work on some heavier atoms. Bohr returned to Copenhagen to continue working on his theory which he completed to his satisfaction in and around July of 1913. The University recommended his name for a chair in theoretical physics, he expected his position to be confirmed within a year. It wasn’t to be. He spent the next four years working with Rutherford and his group yet again, he enjoyed his time with the group immensely, participating in many break through activities.

His completed theory of the atom gave us the clue as to where, exactly, electrons were found in an atom. He stated that electrons traveled on fixed energy levels. Sort of like a ladder, these electrons could change orbits but they would always be found in an orbit and there would always be a certain number of electrons in the orbital.

Changing Energy Levels

The fact that there were certain orbits and energies in an atom was part of Bohr’s theory. When these energies change levels there is a different color given off.

Orbits were the key to Bohr’s theory

Bohr Model of the Atom

• Outline– Emission spectrum of atomic hydrogen.– The Bohr model.

– Extension to higher atomic number.

Photon Emission• Relaxation from

one energy level to another by emitting a photon.

• With DE = hc/l

• If l = 440 nm, DE = 4.5 x 10-19 J

Em

issi

on

Emission spectrum of H “Continuous” spectrum

“Quantized” spectrum

Any DE ispossible

Only certain DE areallowed

E E

Emission spectrum of H

Light Bulb

Hydrogen Lamp

Quantized, not continuous

Emission spectrum of H

We can use the emission spectrum to determine the energy levels for the hydrogen atom.

Balmer Model• Joseph Balmer (1885) first noticed that

the frequency of visible lines in the H atom spectrum could be reproduced by:

1

22

1

n2n = 3, 4, 5, …..

• The above equation predicts that as n increases, the frequencies become more closely spaced.

Rydberg Model• Johann Rydberg extends the Balmer model

by finding more emission lines outside the visible region of the spectrum:

Ry1

n12

1

n22

n1 = 1, 2, 3, …..

• This suggests that the energy levels of the H atom are proportional to 1/n2

n2 = n1+1, n1+2, …

Ry = 3.29 x 1015 1/s

The Bohr Model• Niels Bohr uses the emission spectrum of

hydrogen to develop a quantum model for H.

• Central idea: electron circles the “nucleus” in only certain allowed circular orbitals.

• Bohr postulates that there is Coulombic attraction between e- and nucleus. However, classical physics is unable to explain why an H atom doesn’t simply collapse.

The Bohr Model (cont.)• Bohr model for the H atom is capable of

reproducing the energy levels given by the empirical formulas of Balmer and Rydberg.

E 2.178x10 18JZ 2

n2

Z = atomic number (1 for H)

n = integer (1, 2, ….)

• Ry x h = -2.178 x 10-18 J (!)

The Bohr Model (cont.)

E 2.178x10 18JZ 2

n2

• Energy levels get closer together as n increases

• at n = infinity, E = 0

The Bohr Model (cont.)

• We can use the Bohr model to predict what DE is for any two energy levels

E E final E initial

E 2.178x10 18J1

n final2

( 2.178x10 18J)

1

ninitial2

E 2.178x10 18J1

n final2

1

ninitial2

The Bohr Model (cont.)

• Example: At what wavelength will emission from n = 4 to n = 1 for the H atom be observed?

E 2.178x10 18J1

n final2

1

ninitial2

1 4

E 2.178x10 18J 11

16

2.04x10 18J

E 2.04x10 18J hc

9.74x10 8m97.4nm

The Bohr Model (cont.)

• Example: What is the longest wavelength of light that will result in removal of the e- from H?

E 2.178x10 18J1

n final2

1

ninitial2

1

E 2.178x10 18J 0 1 2.178x10 18J

E 2.178x10 18J hc

9.13x10 8m91.3nm

Extension to Higher Z• The Bohr model can be extended to any single electron system….must keep track of Z (atomic number).

• Examples: He+ (Z = 2), Li+2 (Z = 3), etc.

E 2.178x10 18JZ 2

n2

Z = atomic number

n = integer (1, 2, ….)

Extension to Higher Z (cont.)

• Example: At what wavelength will emission from n = 4 to n = 1 for the He+ atom be observed?

E 2.178x10 18J Z 2 1

n final2

1

ninitial2

2 1 4

E 2.178x10 18J 4 11

16

8.16x10 18J

E 8.16x10 18J hc

2.43x10 8m24.3nm

H He

Where does this go wrong?

• The Bohr model’s successes are limited:

• Doesn’t work for multi-electron atoms.

• The “electron racetrack” picture is incorrect.

• That said, the Bohr model was a pioneering, “quantized” picture of atomic energy levels.