Consider the following statements :
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below :

Question

Which statistical distribution describes the behavior of identical, indistinguishable particles with half-integral spin?

Answer 1

To determine the correct answer, let's analyze each statement:

A. Atoms of each element emit characteristic spectrum.
This statement is true. Each element emits a specific spectrum of light due to electronic transitions within their atoms. This phenomenon is the basis for techniques such as spectroscopy and is widely used to identify elements.
B. According to Bohr's Postulate, an electron in a hydrogen atom revolves in a certain stationary orbit.
This statement is true. Bohr’s model of the hydrogen atom posits that electrons orbit the nucleus in specific, quantized orbits without emitting radiation, until they transition between these orbits.
C. The density of nuclear matter depends on the size of the nucleus.
This statement is false. The density of nuclear matter is approximately constant, irrespective of the size or mass number of the nucleus. Nucleons are closely packed in the nucleus, giving it a roughly uniform density.
D. A free neutron is stable but a free proton decay is possible.
This statement is false. In fact, a free neutron is unstable and decays into a proton, electron, and antineutrino through the process of beta decay, with a half-life of about 14 minutes. Free protons are stable and there is no observed decay of free protons under normal conditions.
E. Radioactivity is an indication of the instability of nuclei.
This statement is true. Radioactivity occurs when unstable nuclei release energy to become more stable. It is a measure of an atom's nuclear instability.

Considering the above analysis, the correct statements are A, B, and E. Therefore, the correct answer is:

A, B and E only

Answer 2

To determine the correct answer, let's analyze each statement:

A. Atoms of each element emit characteristic spectrum.
This statement is true. Each element emits a specific spectrum of light due to electronic transitions within their atoms. This phenomenon is the basis for techniques such as spectroscopy and is widely used to identify elements.
B. According to Bohr's Postulate, an electron in a hydrogen atom revolves in a certain stationary orbit.
This statement is true. Bohr’s model of the hydrogen atom posits that electrons orbit the nucleus in specific, quantized orbits without emitting radiation, until they transition between these orbits.
C. The density of nuclear matter depends on the size of the nucleus.
This statement is false. The density of nuclear matter is approximately constant, irrespective of the size or mass number of the nucleus. Nucleons are closely packed in the nucleus, giving it a roughly uniform density.
D. A free neutron is stable but a free proton decay is possible.
This statement is false. In fact, a free neutron is unstable and decays into a proton, electron, and antineutrino through the process of beta decay, with a half-life of about 14 minutes. Free protons are stable and there is no observed decay of free protons under normal conditions.
E. Radioactivity is an indication of the instability of nuclei.
This statement is true. Radioactivity occurs when unstable nuclei release energy to become more stable. It is a measure of an atom's nuclear instability.

Considering the above analysis, the correct statements are A, B, and E. Therefore, the correct answer is:

A, B and E only

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