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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3as104

Compare the electron in the $n = 2$ orbit of $He X^{+}$ with that in the $n = 2$ orbit of $H$ . Select the correct statements.

AThe speed in $He X^{+}$ is twice that in $H$
BThe time period in $He X^{+}$ is one quarter of that in $H$
CThe magnitude of the total energy in $He X^{+}$ is twice that in $H$
DThe orbit radius in $He X^{+}$ is half that in $H$

Answer: A, B, D

At fixed

n

:

r \propto 1/ Z

(half),

v \propto Z

(double),

∣ E ∣ \propto Z^{2}

(four times, so 'twice' is wrong),

T \propto 1/ Z^{2}

(one quarter; also

T = 2 π r / v

gives

(1/2) /2 = 1/4

).

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