A mong the following, the correct statement(s) for electrons in an atom is(are)
Correct Answer :
Uncertainty principle rules out the existence of definite paths for electrons.
The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus.
According to Bohr’s model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit.
Solution :
To determine the correct statements among the given choices, let us analyze each statement one by one using the principles of quantum mechanics and the Bohr model of the atom:
1. Analysis of Statement A: "Uncertainty principle rules out the existence of definite paths for electrons."
Heisenberg's Uncertainty Principle states that it is impossible to determine simultaneously and precisely both the position and momentum of a subatomic particle like an electron. Mathematically, it is expressed as:
Because we cannot precisely know both position and momentum at any instant, we cannot define a precise trajectory or a definite path for an electron. Instead, we speak of the probability of finding an electron in a region of space (an orbital). Therefore, this statement is correct.
2. Analysis of Statement B: "The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus."
The energy of an electron that is infinitely far away from the nucleus (at ) is defined as zero, which represents a free electron. As the electron gets closer to the nucleus, it is attracted by the electrostatic force, which stabilizes the system and lowers the energy. Consequently, the energy of an electron bound to the nucleus in any orbital (including the 2s orbital) is negative. Since a negative energy value is less than zero, the energy of an electron in the 2s orbital is lower than that of an electron infinitely far away. Therefore, this statement is correct.
3. Analysis of Statement C: "According to Bohr’s model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit."
According to Bohr's theory, the energy of an electron in a hydrogen-like atom in the n-th orbit is given by:
For the ground state, where , the energy is:
This is the most negative energy value possible for the electron. The lower (more negative) the energy of a system, the more stable it is. Thus, corresponds to the most stable orbit (the ground state). Therefore, this statement is correct.
4. Analysis of Statement D: "According to Bohr’s model, the magnitude of velocity of electrons increases with increase in values of n."
According to Bohr's model, the velocity of an electron in the n-th orbit is given by:
This relationship shows that the velocity of the electron is inversely proportional to the principal quantum number . Therefore, as increases, the magnitude of the velocity of the electron decreases. Consequently, this statement is incorrect.
Conclusion:
The correct statements are Statement A, Statement B, and Statement C.
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