1.8 grams of atoms of hydrogen are excited to radiations. the study of spectra indicates that 27% of atoms are in the third energy level and 15% of atoms ate in the second energy level and rest in the ground state. If the I.P. of H is #21.7*10^(12)#erg?
Warning! Long Answer. 1.
 The quantity of atoms in the second and third energies
 When every atom returns to its ground state, the total amount of energy evolved.
where
(d) Total energy expended
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To solve this problem, we can first find the total number of hydrogen atoms in the sample. Then, we can use the given percentages to calculate the number of atoms in each energy level. After that, we can use the concept of energy levels and the given ionization potential (I.P.) to find the energy of each level. Finally, we can sum up the energies of all the atoms in each level to get the total energy of the system.
Given:
 Mass of hydrogen atoms = 1.8 grams
 Percentage of atoms in the third energy level = 27%
 Percentage of atoms in the second energy level = 15%
 Rest of the atoms are in the ground state
 Ionization potential (I.P.) of hydrogen = 21.7 × 10^(12) erg

Calculate the total number of hydrogen atoms:
 Mass of 1 mole of hydrogen atoms = 2 grams (since hydrogen's atomic mass is approximately 1)
 Number of moles of hydrogen atoms = 1.8 grams / 2 grams/mole = 0.9 moles
 Number of hydrogen atoms = 0.9 moles * Avogadro's number ≈ 0.9 * 6.022 × 10^23

Calculate the number of atoms in each energy level:
 Number of atoms in the third energy level = 27% * Total number of atoms
 Number of atoms in the second energy level = 15% * Total number of atoms
 Number of atoms in the ground state = Total number of atoms  (Atoms in third level + Atoms in second level)

Calculate the energy of each energy level:
 Energy of nth energy level = I.P. / n^2 (where n is the principal quantum number)

Calculate the total energy of the system by summing up the energies of all atoms in each energy level.

Substitute the given values into the equations and solve for the total energy of the system.
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