Question

Wavelength of high energy transition of $H$-atom is $91.2 nm$. Calculate the corresponding wavelength of $H{e^ + }$ ion.
A. $91.2 nm$
B. $22.8 nm$
C. $45.6 nm$
D. $182.4 nm$
E. $364.8 nm$

Answer 1

Hint: Energy transition is an extensive structural exchange in an energy machine. Historically, these changes had been driven by way of the call for and availability of different fuels. The modern transition to renewable strength, and perhaps different forms of sustainable power, differs because it is essentially driven with the aid of a recognition that global carbon emissions have to be introduced to, and in view that fossil fuels are the largest unmarried source of carbon emissions, we must change electricity systems worldwide to replace fossil fuels.

Formula used:
$1/x = R{Z^2} \times [1/{(n_1)^2} - 1/{(n_2)^2}]$

Complete step by step solution:
We know, Wavelength formula is-
     $1/x = R{Z^2} \times [1/{(n_1)^2} - 1/{(n_2)^2}]$
                                                                   Where $x$=wavelength
 Now according to question,
$1/91.2 = R{(1)^2} \times [1/{(n_1)^2} - 1/{(n_2)^2}]$ from hydrogen (1)
$1/x = R{(2)^2} \times [1/{(n_1)^2} - 1/{(n_2)^2}]$ from helium()
Line transition is same for both equation
So eq(1)/eq(2)
Then we get
$x/91.2 = 1/4$
$x = 22.8$

So, the correct answer is B.

Additional information:
Historic power transitions are most broadly described by means of Vaclav Smil. Contemporary electricity transitions vary in phrases of motivation and objectives, drivers and governance. The layout of the world's electricity systems has modified extensively over time. Until the Fifties, the economic mechanism at the back of power structures became neighborhood in preference to international. As improvement advanced, extraordinary national systems became an increasing number of incorporated becoming the massive, global systems visible these days. Historical transition charges of energy structures have been appreciably studied. While ancient power transitions had been commonly protracted affairs, unfolding over many many years, this doesn't always maintain proper for the present power transition, that's unfolding underneath very distinctive coverage and technological situations.

Note: An instance of transition in the direction of sustainable energy is the shift by using Germany (Energiewende) and Switzerland, to decentralized renewable electricity, and energy efficiency. Although thus far those shifts had been changing nuclear power, their declared intention changed into the coal segment-out, decreasing non-renewable electricity assets