Answer

Verified

429.6k+ views

**Hint:**The ionization energy of the shell is the negative of the energy of the shell that is $I.E = - {E_1}$ The energy for the nth main shell is given by the following relation

${E_n} = \dfrac{{{E_1}}}{{{n^2}}} \times {Z^2}$

where Z is the atomic number, n is the orbit in which the electron is present. We will use this formula in the given question and arrive at the correct answer.

**Complete step by step solution:**

We have been given the ionization energy of hydrogen-like species that is $960\;eV$ so by the following relation $I.E = - {E_1}$ . So accordingly using the formula that is

Energy for an nth main shell of hydrogen atom=Ionization energy of hydrogen atom /${n^2}$

So putting the given values in the equation, we get

$ - 60 = \dfrac{{ - 960}}{{{n^2}}}$

$ \Rightarrow $ $60 = \dfrac{{960}}{{{n^2}}}$

${n^2} = \dfrac{{960}}{{60}} = 16 \Rightarrow n = 4$

Therefore the value of principal quantum number having energy equal to $ - 60$ eV is four

**So, the correct answer is Option C.**

**Additional information:**

For hydrogen-like species, the energy of an electron in the nth orbit is given by ${E_n} = R\dfrac{{{z^2}}}{{{n^2}}}J/atom$ where R is the Rydberg constant which is equal to $2.18 \times {10^{ - 18}}$ .

Also, the ionization energy increases with an increase in atomic number and decreases with a decrease in atomic number due to a decrease in proximity and attractive force with the nucleus.

**Note:**ionization energy is defined as the energy required to remove an electron from the outermost shell of an isolated gaseous atom. For hydrogen-like species, Z is taken to be one and the ionization energy of the species is the negative of the energy of the electron in the ground state.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How do you graph the function fx 4x class 9 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell