For an electron in different orbits of a hydrogen-like ion, which of the following correctly describes the graph of ₁₀(K) plotted against ₁₀(r) , where K is the kinetic energy and r is the orbital radius?

Step-by-step solution

The kinetic energy K of an electron in a hydrogen-like ion is given by: K = 1 4 ₀ Ze^2 2r This shows that K is inversely proportional to r , which can be written as K = C r , where C is a positive constant. Taking the logarithm to the base 10 on both sides gives: ₁₀(K) = ₁₀(C) - ₁₀(r) Comparing this with the equation of a straight line, y = mx + c , where y = ₁₀(K) and x = ₁₀(r) , we get the slope m = -1 . Thus, the graph is a straight line with a slope of -1 . Answer: A straight line with a slope of -1