# The magnesium atom has speciﬁc energy levels

Astronomy 4: HW #3Due date: Tuesday, April 21st1. Magnesium Energy LevelsThe magnesium atom has speciﬁc energy levels, which correspond to diﬀerent arrangements ofthe electrons around the nucleus. As an electron moves between the diﬀerent energy levels ofmagnesium, photons can be absorbed (transition from a lower to an upper level) or emitted(transition from an upper to a lower level).(a) Level 3 in the magnesium atom is at an energy diﬀerence of 4.3458 eV above the groundstate (level 1). Express this energy diﬀerence in terms of Joules.(b) A photon with the right wavelength will cause an electron in a magnesium atom which isin the ground state (level 1) to jump up to level 3. What is this wavelength?(c) What color of light does the wavelength from part (b) correspond to?2. SunspotsSunspots typically have temperatures of Tspot = 4500 K. At the same time, the non-sunspotregions of the solar photosphere have an average temperature of Tsun = 5800 K.(a) Using the Stefan-Boltzmann law, calculate the ratio between the radiation ﬂux (i.e., Joules/s/m2 )emitted by typical sunspot regions and non-sunspot regions.(b) Using Wienâs Law, calculate the wavelength at which the sunspot thermal spectrum peaks.Compare this wavelength with the one at which the non-sunspot thermal spectrum peaks.3. Hydrogen Fusion in the Sun(a) The solar luminosity is the amount of energy emitted by the Sun per unit time. Based onthe solar luminosity, how many kilograms of hydrogen does the Sun fuse every second?(b) Based on the total mass of the Sun, roughly 75% of which was hydrogen when the Sunformed, and roughly 13% of which is ever available for hydrogen fusion in the core, estimatehow long the Sun can sustain hydrogen fusion. For this estimate, assume that the Sun has hada constant luminosity as a function of time, and express your answer in years.

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