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The wavelength of a certain line in Balmer series is observed to be 4341 Å. To what value of ‘n’ does this correspond?The wavelength of a certain line in Balmer series is observed to be 4341 Å. To what value of ‘n’ doesthis correspond?

sushrut Mukherjee , 13 Years ago
Grade 11
anser 1 Answers
Askiitians Tutor Team

Last Activity: 23 Days ago

To determine the value of 'n' corresponding to the observed wavelength of 4341 Å in the Balmer series, we can use the Rydberg formula. The Balmer series describes the spectral lines of hydrogen when an electron transitions from a higher energy level (n) to the second energy level (n=2). The Rydberg formula for the wavelengths of these transitions is given by:

Rydberg Formula

The formula is expressed as:

1/λ = R_H (1/2² - 1/n²)

Where:

  • λ is the wavelength of the emitted light.
  • R_H is the Rydberg constant, approximately 1.097 × 107 m-1.
  • n is the principal quantum number of the higher energy level (n > 2).

Step-by-Step Calculation

First, we need to convert the wavelength from angstroms to meters for consistency with the Rydberg constant:

4341 Å = 4341 × 10-10 m = 4.341 × 10-7 m.

Next, we can rearrange the Rydberg formula to solve for 'n':

1/n² = 1/2² - 1/(R_H * λ)

Now, substituting the known values:

1/n² = 1/4 - 1/(1.097 × 107 m-1 * 4.341 × 10-7 m)

Calculating the second term:

1/(1.097 × 107 * 4.341 × 10-7) = 1/(4.77) ≈ 0.209.

Now, substituting this back into the equation:

1/n² = 0.25 - 0.209 = 0.041.

Taking the reciprocal gives:

n² = 1/0.041 ≈ 24.39.

Finally, taking the square root gives:

n ≈ 4.94.

Determining the Principal Quantum Number

Since 'n' must be a whole number, we round 4.94 to the nearest integer, which is 5. Therefore, the value of 'n' corresponding to the observed wavelength of 4341 Å in the Balmer series is:

n = 5

Summary

In summary, the observed wavelength of 4341 Å corresponds to a transition from the fifth energy level (n=5) to the second energy level (n=2) in the hydrogen atom's Balmer series. This process illustrates how energy levels in atoms are quantized and how they emit specific wavelengths of light when electrons transition between these levels.

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