Which of the following is true ?

Options

A. (1) The half -filled and full-filled electronic configuration are less stable than the other configuration having the same number of electron.
B. (2) The symbol 's' for the orbitals having `l = 0` has its origin from the term spherical symmetrical.
C. (3) The increasing order for the value of e/m (charge /mass) for electron (e ) proton (p) neutron (n) and alpha particle (a) is : `n > a > p > e`
D. (4) The energy of photon having wavelength `800 nm` is larger than having `400 nm`.

Explanation

To determine which of the given statements is true, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** The half-filled and full-filled electronic configurations are less stable than the other configurations having the same number of electrons.

**Analysis:** This statement is incorrect. Half-filled and fully filled electronic configurations are actually more stable due to symmetry and exchange energy. For example, in the case of chromium (atomic number 24), the configuration 3d5 4s1 is more stable than the expected 3d4 4s2 configuration. Therefore, this statement is false.

### Step 2: Analyze the Second Statement
**Statement:** The symbol 's' for the orbitals having l = 0 has its origin from the term spherical symmetrical.

**Analysis:** This statement is correct. The 's' orbital corresponds to the azimuthal quantum number l = 0, and these orbitals are indeed spherical and symmetrical around the nucleus. Thus, this statement is true.

### Step 3: Analyze the Third Statement
**Statement:** The increasing order of the value of e/m (charge to mass ratio) for electron, proton, neutron, and alpha particle is neutron, then alpha, then proton, then electron.

**Analysis:** This statement is incorrect. The charge to mass ratio for a neutron is 0 (since it has no charge), for an alpha particle is 0.5, for a proton is approximately 1.0, and for an electron is much higher (approximately 1.76 x 10^11 C/kg). Therefore, the correct increasing order is electron > proton > alpha > neutron, making this statement false.

### Step 4: Analyze the Fourth Statement
**Statement:** The energy of a photon having a wavelength of 800 nm is larger than that of a photon having a wavelength of 400 nm.

**Analysis:** This statement is incorrect. Energy is inversely proportional to wavelength (E ∝ 1/λ). Therefore, a photon with a wavelength of 400 nm has higher energy than one with a wavelength of 800 nm. Thus, this statement is false.

### Conclusion
After analyzing all the statements, we find that the only true statement is the second one regarding the 's' orbital.

**Final Answer:** The true statement is: "The symbol 's' for the orbitals having l = 0 has its origin from the term spherical symmetrical."

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