Be sure to answer all parts. solving the rydberg equation for energy change gives δe = r[infinity]hc [ 1 n12 − 1 n22 ] where the rydberg constant r[infinity] for hydrogen-like atoms is 1.097 × 107 m−1 z2, and z is the atomic number.(a) calculate the energies needed to remove an electron from the n = 1 state and the n = 3 state in the li2+ ion. n = 1 × 10 j n = 3 × 10 j (enter your answer in scientific notation.(b) what is the wavelength (in nm) of the emitted photon in a transition from n = 3 to n = 1?

Explanation:

Utilizing Rydber's  equation:

ΔE = Z²Rh ( 1/n₁² - 1/n₂²) and substituting the values given ( using the Rydbers constant value in Joules ), we have

n=1 to n= infinity

ΔE = 3² x (1/1² - 0) x 2.18 x 10⁻^18 J = 2.0 x 10⁻¹⁷ J      (1/infinity is zero)

n= 3 to n= infinity

ΔE = 3² x (1/3² - 0) x 2.18 x 10⁻^18 J = 2.28 x 10^-18 J

b.  The wavelength of the emitted can be obtained again by using Rydberg's equation but this time use the constant value 1.097 x 10⁷ m⁻¹ given in the problem .

1/λ = Z²Rh (1/n₁² - 1/n₂²) 10 ⁻¹ = 3² x 1.097 x 10⁷ m⁻¹ x (1/1² - 1/3²) m⁻¹

1/λ =8.8 x 10⁷ m⁻¹ ⇒  λ =1.1 x 10^-8 m

λ = 1.1 x 10^-8 m x 1 x 10⁹ nm/m = 11 nm

the answer is c

tell me if wrong