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.