Answer

Verified

35.1k+ views

**Hint:**For this we need to know the formula of energy of the hydrogen atom given by Bohr’s model. According to the formula, the energy of a hydrogen atom can never be positive. To calculate ground state energy put \[n\] equals to 1 and for the first excited state put \[n{\text{ = 2}}\]and so on.

Formula used: \[{{\text{E}}_{\text{n}}} = - \dfrac{1}{{{{\text{n}}^{\text{2}}}}} \times 13.6{\text{ eV}}\]

Where, \[{{\text{E}}_{\text{n}}}\]is energy of \[{{\text{n}}^{{\text{th}}}}\] state, \[{\text{n}}\] is the number of stationary state\[(1,2,3......)\].

**Complete step by step solution:**

The above question is based on the Bohr model of Hydrogen atom. It assumes that electrons revolve in certain stationary orbits and the whole value of energy is quantized or fixed. Each energy level has fixed energy and the electron exactly needs to have that amount of energy if it wants to circulate in that particular orbit. The energy of hydrogen atom is given by the formula:

\[{{\text{E}}_{\text{n}}} = - \dfrac{1}{{{{\text{n}}^{\text{2}}}}} \times 13.6{\text{ eV}}\]

As we know \[n\] represents a natural number and hence can never be negative. So clearly the energy of each of the states will be negative. So option A and D stands eliminated here. Now let us put the value of \[n\] one by one and see the values:

Putting \[n{\text{ = 1}}\] we will get,

\[{{\text{E}}_{\text{n}}} = - \dfrac{1}{{{1^2}}} \times 13.6{\text{ eV = - 13}}{\text{.6 eV}}\]

For \[n{\text{ = 2}}\]

\[{{\text{E}}_{\text{n}}} = - \dfrac{1}{{{2^2}}} \times 13.6{\text{ eV = - 3}}{\text{.4 eV}}\]

**Hence, the correct option is option C.**

**Note:**We do not start from \[n{\text{ = 0}}\] to calculate ground state of hydrogen, because in that case the value of ground state energy will be infinite. And this is not possible according to Zero point theorem which states that the lowest possible energy of an element should be finite. Hence, for hydrogen we always start with \[n{\text{ = 1}}\]

Recently Updated Pages

To get a maximum current in an external resistance class 1 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main

Find the points of intersection of the tangents at class 11 maths JEE_Main

For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

Other Pages

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Which of the following sets of displacements might class 11 physics JEE_Main

Oxidation state of S in H2S2O8 is A 6 B 7 C +8 D 0 class 12 chemistry JEE_Main

What is the pH of 001 M solution of HCl a 1 b 10 c class 11 chemistry JEE_Main

The correct IUPAC name of the given compound is A isopropylbenzene class 11 chemistry JEE_Main