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The first spectral line in the Balmer series for hydrogen is emitted when an electron hops from the energy level with quantum number n=3 to the one with quantum number m=2 in the hydrogen atom. (a) If we assume that the nucleus of the atom has infinite mass, what is the wavelength of this spectral line in nm with three decimal digits? Is the line visible? If so, what color is it? (b) What is the wavelength (also with three decimal digits) if we include the reduced mass correction for the finite mass of the nucleus. (c) Suppose the reduced mass u changes by a small amount A. Show that the wavelength changes by a corresponding amount Aà that satisfies A./A=-Au/u.

The first spectral line in the Balmer series for hydrogen is emitted when an electron hops from the energy level with quantum number n=3 to the one with quantum number m=2 in the hydrogen atom. (a) If we assume that the nucleus of the atom has infinite mass, what is the wavelength of this spectral line in nm with three decimal digits? Is the line visible? If so, what color is it? (b) What is the wavelength (also with three decimal digits) if we include the reduced mass correction for the finite mass of the nucleus. (c) Suppose the reduced mass u changes by a small amount A. Show that the wavelength changes by a corresponding amount Aà that satisfies A./A=-Au/u.

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The first spectral line in the Balmer series for hydrogen is emitted when an electron hops from the energy level with quantum number n=3 to the one with quantum number m=2 in the hydrogen atom. (a) If we assume that the nucleus of the atom has infinite mass, what is the wavelength of this spectral line in nm with three decimal digits? Is the line visible? If so, what color is it? (b) What is the wavelength (also with three decimal digits) if we include the reduced mass correction for the finite mass of the nucleus. (c) Suppose the reduced mass u changes by a small amount Au. Show that the wavelength changes by a corresponding amount Aà that satisfies A./2=-Aµ/µ. (d) Find the wavelength shift in the first Balmer line between hydrogen and deuterium. It was precisely this small wavelength shift that led to the first discovery of deuterium in 1931.
Transcribed Image Text:The first spectral line in the Balmer series for hydrogen is emitted when an electron hops from the energy level with quantum number n=3 to the one with quantum number m=2 in the hydrogen atom. (a) If we assume that the nucleus of the atom has infinite mass, what is the wavelength of this spectral line in nm with three decimal digits? Is the line visible? If so, what color is it? (b) What is the wavelength (also with three decimal digits) if we include the reduced mass correction for the finite mass of the nucleus. (c) Suppose the reduced mass u changes by a small amount Au. Show that the wavelength changes by a corresponding amount Aà that satisfies A./2=-Aµ/µ. (d) Find the wavelength shift in the first Balmer line between hydrogen and deuterium. It was precisely this small wavelength shift that led to the first discovery of deuterium in 1931.
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