Question

Among the following, the correct statement(s) for electrons in an atom is(are)

• A. Uncertainty principle rules out the existence of definite paths for electrons.
• 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.
• 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.
• D. According to Bohr's model, the magnitude of velocity of electrons increases with increase in values of n.

Answer 1

The Correct Option is A, B, C

Step 1: Evaluate Statement (A) 

• The uncertainty principle states that the exact position and momentum of an electron cannot be simultaneously determined.
• This implies that electrons do not have well-defined paths or trajectories.
• Hence, statement (A) is correct.

Step 2: Evaluate Statement (B)

• Electrons in orbitals closer to the nucleus (e.g., 2s) have lower energy compared to electrons at a large distance (infinitely far away) from the nucleus.
• This is because the potential energy of attraction between the electron and the nucleus decreases as the electron moves closer.
• Hence, statement (B) is correct.

Step 3: Evaluate Statement (C)

According to Bohr’s model, the energy of an electron in the \( n \)-th orbit is given by:

\[ E = -\frac{13.6Z^2}{n^2} \text{ eV/atom}, \]

where \( Z \) is the atomic number.

• For \( n = 1 \), the energy is most negative, corresponding to the most stable orbit.
• Hence, statement (C) is correct.

Step 4: Evaluate Statement (D)

According to Bohr’s model, the velocity of an electron in the \( n \)-th orbit is given by:

\[ V = V_0 \frac{Z}{n}, \]

where \( V_0 \) is a constant.

• As \( n \) increases, the velocity of the electron decreases because it becomes less tightly bound to the nucleus.
• Hence, statement (D) is incorrect.

Conclusion:

The correct statements are: (A, B, C).

Answer 2

To solve the problem, we need to evaluate each given statement about electrons in an atom and identify which are correct.

1. Uncertainty Principle and Electron Paths:
The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the exact position and momentum of an electron.
Therefore, electrons do not have definite paths (or orbits), ruling out the classical idea of fixed electron paths.
Statement 1 is correct.

2. Energy of Electron in 2s Orbital vs. Electron at Infinite Distance:
The energy of an electron in any bound orbital (such as 2s) is negative and lower than the energy of a free electron at infinite distance (which is zero).
Thus, electron in 2s orbital has energy less than that of electron infinitely far.
Statement 2 is correct.

3. Most Negative Energy Value in Bohr’s Model:
Bohr’s model gives the energy levels as \(E_n = -\frac{13.6\, \text{eV}}{n^2}\). The lowest energy (most negative) corresponds to \(n=1\), which is the most stable orbit.
Statement 3 is correct.

4. Velocity of Electron and Quantum Number n in Bohr’s Model:
According to Bohr’s model, velocity \(v_n = \frac{Z e^2}{2 \varepsilon_0 h n}\), which means velocity decreases as \(n\) increases.
Therefore, velocity decreases with increasing \(n\).
Statement 4 is incorrect.

Final Answer:
Statements 1, 2, and 3 are correct; Statement 4 is incorrect.