the energy associated with the first orbit in the hydrogen atom is -2.1 into 10 to the power minus 18 jul per atom what is the energy associated with the fifth orbit
Answers
n = 1 Z = 1 for Hydrogen atom...
energy = - Z² 13.6 / n² eV
= - 13.6 * 1² * 1.602 * 10⁻¹⁹ / n² Joules
= - 2.178 * 10⁻¹⁸ / n² Joules
the energy is inversely proportional to the square of n or orbit or shell number..
for the 5 th orbit:
energy = - 2.178 * 10⁻¹⁸ / 25 Joules = - 8.712 * 10⁻²⁰ Joules
= 0.544 eV
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Bohr's radius for the 5th Orbit:
m v² / R = K Ze * e / R² => v² = K Z e² / (m R) --- (1)
angular momentum = m v R = n h / 2π
=> v = n h / (2 π m R) --- (2)
from (1) and (2): n² h² / (4π² m² R²) = K Z e² / (m R)
=> R = n² h² / (4π² m K e² Z) --- (3)
R = Bohr' radius for an atom of atomic number Z,
n = orbit number = principal quantum number = 5
h = Planck's constant = 6.626 * 10⁻³⁴ units
K = 1/(4πε₀) = 9 * 10⁹ units = Coulomb's constant
Z = 1 for Hydrogen
m = mass of an electron = 9.1 * 10⁻³¹ kg
e = charge on the electron = 1.602 * 10⁻¹⁹ C
Radius for the first orbit n = 1 is:
R = 0.00529 * 10⁻⁸ meters = 5.29 * 10⁻¹¹ meters
= 0.529 Angstroms: °A
Radius for the n = 5 orbit is:
R = 5² * 5.29 * 10⁻¹¹ m = 13.227 °A
Answer:
5^2*5.29*10^-11*m=13.227
Explanation: