When an electron jumps from the 4th orbit to the 2nd orbit which series line does it get?

Balmer series

are u sure? are there any possibility of being paschen series?

When an electron jumps from the 4th orbit to the 2nd orbit, it emits energy in the form of light. This energy corresponds to a specific wavelength or color of light. The wavelength can be determined using the Rydberg formula:

1/λ = R × [(1/n₁²) - (1/n₂²)]

where λ is the wavelength of light, R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹), n₁ is the initial orbit number (4 in this case), and n₂ is the final orbit number (2 in this case).

To find the wavelength, substitute the values into the formula:

1/λ = (1.097 × 10^7 m⁻¹) × [(1/4²) - (1/2²)]

Simplifying the equation:

1/λ = (1.097 × 10^7 m⁻¹) × [(1/16) - (1/4)]

1/λ = (1.097 × 10^7 m⁻¹) × (1/16 - 1/4)

1/λ = (1.097 × 10^7 m⁻¹) × (1/16 - 4/16)

1/λ = (1.097 × 10^7 m⁻¹) × (-3/16)

1/λ = - (3.308 × 10^6 m⁻¹)

Now, take the reciprocal of both sides to find the wavelength:

λ = -1/(3.308 × 10^6 m⁻¹)

Calculating the wavelength:

λ ≈ -3.02 × 10⁻⁷ m

Note: The negative sign indicates that the light is in the ultraviolet range, as jumps from higher energy levels to lower energy levels release energy in the form of photons with wavelengths in the ultraviolet or higher energy range.

So, the electron emits ultraviolet light when it jumps from the 4th orbit to the 2nd orbit.