Question

the energy of an electron in an orbit of hydrogen like ion with an orbit radius 52.9 pm in Joules is (ground state energy of electron in hydrogen atom is -2.18×10^-18 J​

Answer 1

energy of electron in joules is -2.18 × 10^-18

we have to find the energy of an electron in an orbit of hydrogen ion with an orbit radius 52.9 pm .

here given, r_n = 52.9 pm ........(1)

using Bohr's atomic theory,

r_n = n²h²/4π²mZe²

= (h²/4π²me²) n²/Z

here h = 6.63 × 10¯³⁴ Js , m = 9.1 × 10¯³¹ Kg , e = 1.6 × 10^-19 C

we get, r_n = 52.9 × n²/Z pm ......(2)

now from equations (1) and (2) we get,

52.9 = 52.9 × n²/1 [ Z = 1 for hydrogen ion ]

⇒ n = 1

now energy of electron in nth orbit is given by, E = -2.18 × 10^-18 Z²/n² J

= -2.18 × 10^-18 × 1²/1² J

= -2.18 × 10^-18 J

therefore, energy of electron in joules is -2.18 × 10^-18

Answer 2

Answer:

energy of electron in joules is -2.18 × 10^-18

we have to find the energy of an electron in an orbit of hydrogen ion with an orbit radius 52.9 pm .

here given, r_n = 52.9 pm ........(1)

using Bohr's atomic theory,

r_n = n²h²/4π²mZe²

= (h²/4π²me²) n²/Z

here h = 6.63 × 10¯³⁴ Js , m = 9.1 × 10¯³¹ Kg , e = 1.6 × 10^-19 C

we get, r_n = 52.9 × n²/Z pm ......(2)

now from equations (1) and (2) we get,

52.9 = 52.9 × n²/1 [ Z = 1 for hydrogen ion ]

⇒ n = 1

now energy of electron in nth orbit is given by, E = -2.18 × 10^-18 Z²/n² J

= -2.18 × 10^-18 × 1²/1² J

= -2.18 × 10^-18 J

therefore, energy of electron in joules is -2.18 × 10^-18