TOPIC: NIELS BOHR’S ATOMIC MODEL 1 . ​ According to the Bohr’s orbit model, electrons may be present at any of the allowed orbits whose energy is defined by the expression: E n = -2.179 x 10 -18 J(Z 2 / n 2 ), where Z is the atomic number or nuclear charge, and n = 1, 2, 3, .. is called the quantum number . For hydrogen atom that has Z = 1, the energy of the first four orbits are given below: ​ —————————————————————————— ​ Quantum # ​ ​ Energy values _____ ____________ ​ n = 1 ​ ​ ​ -2.18 x 10 -18 J ( lowest energy level or “ ground state ”) ​ n = 2 ​ ​ ​ -5.45 x 10 -19 J ( first excited state ) ​ n = 3 ​ ​ ​ -2.42 x 10 -19 J ( second excited state ) ​ n = 4 ​ ​ ​ -1.36 x 10 -19 J ( third excited state ) ​ —————————————————————————— (Speed of light, c = 2.998 x 10 8 m/ s; h = 6.626 x 10 -34 J.s. ; 1 nm = 10 -9 m; 1 m = 10 9 nm) (a) Why are the energy values negative? (b) An electron in hydrogen atom jumps from the first orbit ( n = 1) to the 4 th orbit ( n = 4). What is the energy change (  E) for the electron? Does the electron gain or lose energy? Explain. What are the frequency (  ) and wavelength (  ) of light that would provide just enough energy for the electron to make this jump? In what spectral region is this light found, uv , visible, or infra-red region? (c) The same electron then jumps from the 4 th orbit to the second orbit ( n = 2). What is the energy change (  E) for the electron in this jump? Does the electron gain or lose energy? Explain. What are the frequency (  ) and wavelength (  ) of light emitted from this energy change? In what spectral region is this light emitted, uv , visible, or infra-red region?

 

 

TOPIC: NIELS BOHR’S ATOMIC MODEL

1.​According to the Bohr’s orbit model, electrons may be present at any of the allowed orbits whose energy is defined by the expression: En = -2.179 x 10-18 J(Z2/n2), where Z is the atomic number or nuclear charge, and n = 1, 2, 3, ..is called the quantum number. For hydrogen atom that has Z = 1, the energy of the first four orbits are given below: 

​——————————————————————————

​Quantum #​​    Energy values_________________

​n = 1​​​-2.18 x 10-18 J  (lowest energy level or “ground state”)

​n = 2​​​-5.45 x 10-19 J  (first excited state)

​n = 3​​​-2.42 x 10-19 J  (second excited state)

​n = 4​​​-1.36 x 10-19 J  (third excited state)

​——————————————————————————

(Speed of light, c = 2.998 x 108 m/s;  h = 6.626 x 10-34 J.s.;  1 nm = 10-9 m;  1 m = 109 nm)

 

(a) Why are the energy values negative?  

 

 

 

(b) An electron in hydrogen atom jumps from the first orbit (n = 1) to the 4th orbit (n = 4). What is the energy change (E) for the electron? Does the electron gain or lose energy? Explain. What are the frequency () and wavelength () of light that would provide just enough energy for the electron to make this jump? In what spectral region is this light found, uv, visible, or infra-red region?

 

 

 

      

 

(c) The same electron then jumps from the 4th orbit to the second orbit (n = 2). What is the energy change (E) for the electron in this jump? Does the electron gain or lose energy? Explain. What are the frequency () and wavelength () of light emitted from this energy change? In what spectral region is this light emitted, uv, visible, or infra-red region?