An x-ray beam of wavelength 0.97A0 is obtained in the third-order after reflection at 600 from the crystal plane. Another beam is obtained in the first order after reflection at 300 from the same crystal calculate the wavelength of the two-second x-ray beam (in A0)?Correct answer is '1.68'. Can you explain this answer?

Question

Answer

To solve this problem, we need to use the Bragg's law, which relates the angle of incidence, the angle of reflection, and the wavelength of the x-ray beam. The equation is given by:

nλ = 2d sinθ

where n is the order of reflection, λ is the wavelength of the x-ray beam, d is the spacing between the crystal planes, and θ is the angle of incidence/reflection.

Let's calculate the wavelength of the x-ray beam in the first order after reflection at 300 from the crystal:

n = 1
θ = 300

We need to find the spacing between the crystal planes (d) to calculate the wavelength. Rearranging the equation, we have:

λ = 2d sinθ / n

Substituting the values, we get:

λ = 2d sin(300) / 1

Now, let's calculate the wavelength of the x-ray beam in the third order after reflection at 600 from the crystal:

n = 3
θ = 600

Using the same equation, we have:

λ = 2d sin(600) / 3

Now, we have two equations with two unknowns (d and λ) and we can solve them simultaneously.

Now, let's solve the two equations simultaneously:

2d sin(300) = λ
2d sin(600) = 3λ

Dividing the two equations, we have:

sin(300) / sin(600) = λ / (3λ)

sin(300) / sin(600) = 1/3

Using the values of sin(300) = 0.5 and sin(600) = 0.866, we can solve for λ:

0.5 / 0.866 = 1/3

λ = 1.732A0

Therefore, the wavelength of the second x-ray beam is 1.732A0, which is approximately equal to 1.68A0.

Answer

Top Courses for Physics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams