Select the correct statement (s) :
(a)In wave mechanical model, the energy of electron in the orbital remains constant
(b)`d_(xy)` orbital is lies in yz plane
(c)Nodal planes are yz and xy in `d_(x^(2)-y^(2))` orbital
(d)Rest mass of photon is zero and increases with its velocity

Options

A. In wave mechanical model, the energy of electron in the orbital remains constant
B. `d_(xy)` orbital is lies in yz plane
C. Nodal planes are yz and xy in `d_(x^(2)-y^(2))` orbital
D. Rest mass of photon is zero and increases with its velocity

Answer

To solve the question, we need to evaluate each statement one by one and determine if it is correct or incorrect.

### Step 1: Evaluate Statement (a)
**Statement:** In wave mechanical model, the energy of electron in the orbital remains constant.

**Analysis:** In the wave mechanical model, electrons are described by wave functions, and their positions are not fixed. The energy levels of electrons can change due to various factors, such as interactions with other particles or external fields. Therefore, this statement is **incorrect**.

### Step 2: Evaluate Statement (b)
**Statement:** `d_(xy)` orbital lies in the yz plane.

**Analysis:** The `d_(xy)` orbital has lobes that lie in the xy plane, not the yz plane. The nodal planes for the `d_(xy)` orbital are indeed the xz and yz planes, where the probability of finding an electron is zero. Thus, this statement is **incorrect**.

### Step 3: Evaluate Statement (c)
**Statement:** Nodal planes are yz and xy in `d_(x^(2)-y^(2))` orbital.

**Analysis:** The `d_(x^(2)-y^(2))` orbital has lobes along the x and y axes, and the nodal planes are indeed the yz and xy planes. This means that the probability of finding an electron is zero in these planes. Therefore, this statement is **correct**.

### Step 4: Evaluate Statement (d)
**Statement:** Rest mass of photon is zero and increases with its velocity.

**Analysis:** The rest mass of a photon is indeed zero, and it does not increase with velocity. In fact, photons always travel at the speed of light in a vacuum, and their relativistic mass is not defined in the same way as for objects with mass. Thus, this statement is **incorrect**.

### Conclusion
The only correct statement is (c).

### Final Answer:
The correct statement is:
(c) Nodal planes are yz and xy in `d_(x^(2)-y^(2))` orbital.

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