Of the following contributions to the quantum theory of the atom, Planck proposed

options are:

a) a relationship between mass and energy
b) the uncertainty principle
c) matter exhibits wave-particle duality
d) light exhibits wave-particle duality
e) none of the above are correct

is the correct Answer is a)?

No, the correct answer is e) none of the above are correct.

Planck is best known for proposing the concept of quantization of energy, which led to his formulation of the Planck constant and the development of quantum theory. This concept was a significant step in the understanding of the behavior of energy at the atomic and subatomic level, but it is not represented in any of the given options.

No, the correct answer is e) none of the above are correct. Planck's contribution to the quantum theory of the atom was the proposal of quantization, which states that energy is emitted and absorbed in discrete units called quanta.

No, the correct answer is d) light exhibits wave-particle duality.

To arrive at this answer, we can eliminate options a), b), and c) as they are not specific to Planck's contributions to the quantum theory of the atom.

Option a) refers to Einstein's famous equation E=mc^2, which describes the relationship between mass and energy but was not proposed by Planck.

Option b) refers to Heisenberg's uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle was also not proposed by Planck.

Option c) refers to the wave-particle duality of matter, which was introduced later by de Broglie, stating that particles like electrons can exhibit wave-like characteristics. Again, this was not Planck's contribution.

Option d), on the other hand, correctly identifies Planck's contribution to the quantum theory of the atom. In 1900, Planck proposed that light (electromagnetic radiation) consists of discrete packets of energy called quanta or photons. This idea revolutionized our understanding of light and laid the foundation for the development of quantum mechanics.