Anonymous A. answered • 09/29/22

Intuitive, concise, and straightforward science tutoring

**1) We can first use the Rydberg equation to find the energy of the emitted radiation**

E = -R_{H} × [ (1/n_{i}^{2}) - (1/n_{f}^{2}) ]

where R_{H} is the Rydberg constant of 2.18 x 10^{-18} J/electron, n_{i} is the initial energy level, and n_{f} is the final energy level

**2) Let's identify the initial and final energy levels**

The initial energy level, n_{i}, is equal to 5 since the electron was originally in the n=5 energy level.

The final energy level, n_{f}, is equal to 2 since the electron ends up in the n=2 energy level.

**3) We are now ready to solve for the energy of the emitted radiation**

E = -R_{H} × [ (1/n_{i}^{2}) - (1/n_{f}^{2}) ]

E = -2.18 x 10^{-18} J/electron × [ (1/5^{2}) - (1/2^{2}) ]

E = -2.18 x 10^{-18} J/electron × [ (1/25) - (1/4) ] *(The common denominator is 100. We can therefore convert convert 1/25 to 4/100 and 1/4 to 25/100.)*

E = -2.18 x 10^{-18} J/electron × [ (4/100) - (25/100) ]

E = -2.18 x 10^{-18} J/electron × (-21/100) (*Instead of diving by 100 we can instead multiply by 10*^{-2}*)*

E = -2.18 x 10^{-18} J/electron × -21 × 10^{-2}

E = 45.78 x 10^{-20} (*We need to multiply 45.78 by 10*^{-1}* to move the decimal over to the left one place. We then have to also multiply by 10*^{1}* so we aren't actually changing anything.)*

E = 4.578 x 10^{-19} J

**3) We can then use the equation that relates energy to frequency to solve for frequency**

E = h x f

where E is energy, h is Planck's constant of 6.626 x 10^{-34 }J/s, and f is frequency

f = E / h

f = (4.578 x 10^{-19 }J) / 6.626 x 10^{-34 }J/s (*Dividing by 10*^{-34}* is the same as multiplying by 10*^{34}*)*

f = 0.6909 x 10^{15} 1/s (*To move the decimal to the right one, we will multiplying by 10*^{1}*. We then need to multiply by 10*^{-1}* so we aren't actually changing anything.)*

f = 6.909 x 10^{14} Hz (We use the units of Hz since Hz is equal to 1/s)

**4) The frequency of emitted radiation is therefore 6.909 x 10**^{14}** Hz**

Folo D.

oh my gosh! thank you so much!09/30/22