A diffraction grating has $2000$ lines per ${\mathrm{cm}}^{\mathrm{-1}}$. What is the distance between adjacent slits (the grating spacing) in meters?

• A. $2\times {10}^{-5}$ meters
• B. $2\times {10}^{-6}$ meters
• C. $5\times {10}^{-6}$ meters
• D. $5\times {10}^{-5}$ meters

Answer: (C)

Verified step by step guidance

1. Identify the given information: the diffraction grating has 2000 lines per centimeter. This means there are 2000 slits in every 1 cm length.
2. Convert the number of lines per centimeter to lines per meter by multiplying by 100, since 1 meter = 100 centimeters. So, the number of lines per meter is \(2000 \times 100\).
3. Recall that the grating spacing \(d\) is the distance between adjacent slits, which is the reciprocal of the number of lines per meter. Mathematically, \(d = \frac{1}{N}\), where \(N\) is the number of lines per meter.
4. Calculate \(d\) by taking the reciprocal of the number of lines per meter: \(d = \frac{1}{2000 \times 100}\) meters.
5. Express the result in scientific notation to find the grating spacing in meters.