Question

A plane grating has 15000 lines per inch. Find the angle of separation of the 5048 Å lines of helium in second order spectrum

Answer 1

Explanation:

Given A plane grating has 15000 lines per inch. Find the angle of separation of the 5048 Å and 5016 A lines of helium in second order spectrum

• So the wavelengths are given as  
•                               Λ1 = 5016 Angstrom
•                               Λ2 = 5048 Angstrom
•                                K = 2
• Since grating has 15000 lines / inch by converting to cm we get
•               1 inch = 2.54 cm
•                          e = 2.54 / 15000 cm
• Since thete1 and theta2 are the angle of diffraction for second order we get
• 2 Λ1 = e sin theta1
• 2 Λ2 = e sin theta 2
• Now sin theta1 = 2 Λ1 / e
•                            = 2 x 5016 x 10^-8 / 2.54 / 15000
•                            = 2 x 5016 x 10^-8 x 15000 / 2.54
•                            = 2 x 5016 x 15 x 10^-5 / 2.54
•                            = 0.59244
•               Theta = 36.3275
•                           = 36 deg 20’
• Now sin theta2 = 2 Λ2 / e
•                            = 2 x 5048 x 10^-8 / 2.54 / 15000
•                            = 2 x 5048 x 10^-8 x 15000 / 2.54
•                            = 2 x 5048 x 15 x 10^-5 / 2.54
•                            = 0.59622
•               Theta = 36.598
•                           = 36 deg 36’
• Now angle of separation is theta2 – theta1
•                                                 36 deg 36’ – 36 deg 20’
•                                                     = 16’

Reference link will be

https://brainly.in/question/18279916

Answer 2

Answer:

The angle of separation would be 16'.

Explanation:

Given -  Grating - 15000 lines per inch.

              2 lines of Helium  - 5048 and 5016 Å

To find - angle of separation of the lines

Solution -

We are given the 2 wavelengths to be $\lambda_1 = 5016 Å\\\lambda_2 = 5048 Å$

Because we are given the grating to be 15000 per inch, upon converting it to cm, we get e = $\frac{2.54}{15000}$ cm

Now, we have to find the angles of diffraction -

$2 \lambda_1 = e sin \theta_1\\\lambda_2 = e sin \theta_2$

$sin \theta_1 = \frac{2 \lambda_1}{e} \\sin \theta_1 = \frac{2 \times 5016 \times 10^-^8}{\frac{2.54}{15000} } \\\\sin \theta_1 = \frac{2 \times 5016 \times 10^-^8 \times 15000}{2.54} \\\\sin \theta_1 = 0.59244 \\\theta = 36.3275\\ \theta = 36^o 20'$

$sin \theta_2 = \frac{2 \lambda_2}{2} \\\sin \theta_2 = \frac{2 \times 5048 \times 10^-^8}{\frac{2.54}{15000} } \\ sin \theta_2 = \frac{2 \times 5048 \times 10^-^8 \times 15000}{2.54} \\\\\\sin \theta_2 = 0.59622 \\\ \theta = 36.598\\ \theta = 36^0 36'$

Now, we calculate the angle of separation as follows

$\theta_2 - \theta_1 = 36^o36' - 36^o20'\\ \theta_2 - \theta_1 = 16'$

Now angle of separation is 16'.

#SPJ2