Question

A hypothetical NH molecule makes a rotational-level transition from l = 3 to l = 1 and gives off a photon of wavelength 1.740 nm in doing so.

What is the separation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen is 1.67×10−27kg, and the mass of nitrogen is 2.33×10−26kg.

Answer 1

To calculate the separation between the two atoms in the NH molecule, we can convert the photon's wavelength to frequency and use the formula for rotational energy levels of diatomic molecules.

Step-by-step explanation:

To calculate the separation between the two atoms in the NH molecule, we need to first convert the wavelength of the photon to frequency using the equation speed of light = wavelength * frequency. Then, we can use the formula for rotational energy levels of diatomic molecules, which is given by E = (h^2 / 8*pi^2 * I) * (l * (l + 1)), where h is Planck's constant, I is the reduced mass of the system, and l is the quantum number for the rotational level transition.

Given that the wavelength of the photon is 1.740 nm and the masses of hydrogen and nitrogen are provided, we can solve for the frequency. Then, using the rotational energy formula, we can determine the separation between the two atoms.

Answer 2

To find the separation between the two atoms in the NH molecule, we can use the equation for the wavelength of a photon emitted during a rotational-level transition. By rearranging the equation and plugging in the given values, we can calculate the separation.

Step-by-step explanation:

To find the separation between the two atoms in the NH molecule, we need to use the equation for the wavelength of a photon emitted during a rotational-level transition. The equation is given by:

wavelength = 2 * pi * (moment of inertia / reduced mass) * (initial rotational level - final rotational level)

We can rearrange this equation to solve for the separation between the atoms:

separation = reduced mass * (wavelength / (2 * pi * (initial rotational level - final rotational level)))

Now, we can plug in the given values to find the separation. The reduced mass is the mass of nitrogen multiplied by the mass of hydrogen, divided by the sum of their masses. The initial rotational level is 3 and the final rotational level is 1. The wavelength is given as 1.740 nm. Plugging in these values gives:

separation = (2.33 x 10^-26 kg * 1.67 x 10^-27 kg) / (2 * pi * (3 - 1)) * 1.740 x 10^-9 m)

Simplifying this expression gives the separation between the atoms in the NH molecule.