Whats the easy lazy person way to solve this? According to the Bohr model, the allowed energies of the hydrogen atom are given by the equation: E = (-21.7 x 10^-19)/n2 J. From what energy level must an electron fall to the n = 2 state to produce a line at 486.1 nm, the blue-green line in the visible hydrogen spectrum?

A. 4
B. 3
C. 1
D. 5
E. 6

Question

Whats the easy lazy person way to solve this? According to the Bohr model, the allowed energies of the hydrogen atom are given by the equation: E = (-21.7 x 10^-19)/n2 J. From what energy level must an electron fall to the n = 2 state to produce a line at 486.1 nm, the blue-green line in the visible hydrogen spectrum?
  	
 A. 	4 	 	 
B. 	3 		  	 
C. 	1 		  	 
D. 	5 		  	 
E. 	6

anonymous · Answer

Use the Planck relation (E = hv) to calculate the energy of a 486.1 nm photon.  Now graph $$\Delta E =  R_h \left( \frac{1}{2^2} - \frac{1}{n^2} \right)$$on your graphing calculator, or some calculator app on your desktop.  You should be able to pick out the correct n for the E = dE you need by eye.  Then do the calculation to be sure you've got it right.  That way you don't need to do the calculation for all five possibilities.