STATEMENT-1`:` de-Broglie wavelength is not appreciable for molecule`//` atom moving in gaseous state.
STATEMENT -2 `:` Law of uncertainty is not applicable to molecule`//`atom of a gas
STATEMENT-3 `:` Value of spin quantum number is the directional cosine of magnetic moment dueto rotation of electron

Options

A. T T F
B. F T T
C. T F T
D. F F T

Answer

To analyze the given statements and determine their validity, let's break down each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** "de-Broglie wavelength is not appreciable for molecule/atom moving in gaseous state."

- **Explanation:** The de-Broglie wavelength (λ) is given by the formula:
\[ λ = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is its velocity. For molecules and atoms in the gaseous state, although they are larger than electrons, they still exhibit wave-like properties. Therefore, the de-Broglie wavelength can be calculated and is indeed appreciable, especially at the microscopic level.

- **Conclusion:** This statement is **false**.

### Step 2: Analyze Statement 2
**Statement 2:** "Law of uncertainty is not applicable to molecule/atom of a gas."

- **Explanation:** The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the position (Δx) and momentum (Δp) of a particle with absolute precision. The principle applies to all particles, including molecules and atoms in a gas. Therefore, the law of uncertainty is applicable to gaseous atoms and molecules.

- **Conclusion:** This statement is **false**.

### Step 3: Analyze Statement 3
**Statement 3:** "Value of spin quantum number is the directional cosine of magnetic moment due to rotation of electron."

- **Explanation:** The spin quantum number (s) can take values of +1/2 or -1/2, representing the two possible orientations of an electron's spin. The magnetic moment associated with the electron's spin is indeed related to its angular momentum. However, the statement that the spin quantum number is the "directional cosine" of the magnetic moment is misleading. The spin quantum number itself does not represent a directional cosine, but it does relate to the magnetic moment.

- **Conclusion:** This statement is **true**.

### Final Assessment
- **Statement 1:** False
- **Statement 2:** False
- **Statement 3:** True

Thus, the correct option based on the truth values of the statements is **Option 4: False, False, True**.

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