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).