An electrode in Hydrogen atom(ground state) jump to higher energy level x, such that the potential energy of electron becomes half of its total energy at ground state. What is the value of x?

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Solution

We know, Total Energy = Potential Energy/2
i.e. $T . E . = \frac{P . E .}{2}$
Total energy in ground state = T.E. = 13.6 eV
Therefore, Half of Total energy $= P . E (n e w) = \frac{13.6}{2} = 6.8$ eV
At this stage, Total Energy $= \frac{6.8}{2} = 3.4$ eV

Energy at level x is given by = $\frac{13.6}{x^{2}} = 3.4$ eV
x = 2

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An electrode in Hydrogen atom(ground state) jump to higher energy level x, such that the potential energy of electron becomes half of its total energy at ground state. What is the value of x?

We know, Total Energy = Potential Energy/2 i.e. T.E.=P.E.2Total energy in ground state = T.E. = 13.6 eVTherefore, Half of Total energy =P.E(new)=13.62=6.8 eVAt this stage, Total Energy =6.82=3.4 eVEnergy at level x is given by = 13.6x2=3.4 eVx = 2