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Structure Of Atom

Question
CBSEENCH11005370

Calculate the energy required for the process.
He+(g) → He2+ (g) + e-
The ionization energy for the H atom in the ground state is 2.18 x 10-18 J atom-1

Solution

Energy space associated space with space hydroge minus like space species space is space given space by comma
straight E subscript straight n space equals negative 2.18 space straight x space 10 to the power of negative 18 end exponent open parentheses straight Z squared over straight n squared close parentheses space straight J
For space ground space state space of space hydrogen space atom comma space
Energy space is space given space as comma
increment straight E space equals straight E subscript infinity minus straight E subscript 1
0 minus open square brackets negative 2.18 space straight x space 10 to the power of negative 18 end exponent open curly brackets fraction numerator left parenthesis 1 right parenthesis squared over denominator left parenthesis 1 right parenthesis squared end fraction close curly brackets close square brackets space straight x space straight J
increment straight E space equals 2.18 space straight x space 10 to the power of negative 18 end exponent straight J

For space the space given space process comma
He to the power of plus subscript left parenthesis straight g right parenthesis end subscript rightwards arrow space straight H to the power of 2 plus end exponent subscript left parenthesis straight g right parenthesis end subscript space plus straight e to the power of minus
An space electron space is space removed space from space straight n equals 1 space to space straight n equals infinity

increment straight E space equals straight E subscript infinity minus straight E subscript 1
0 minus open square brackets negative 2.18 space straight x space 10 to the power of negative 18 end exponent open curly brackets fraction numerator left parenthesis 2 right parenthesis squared over denominator left parenthesis 1 right parenthesis squared end fraction close curly brackets close square brackets space straight x space straight J

increment straight E space equals 8.72 space straight x space 10 to the power of negative 18 end exponent straight J
The space energy space required space for space the space process.