The circumference of the third orbit of He^+ ion is x m. The de-Broglie wavelength of electron revol — Atomic Structure Chemistry Question

💡 Solution & Explanation

**Step 1 - De Broglie Standing Wave Condition** For an electron in a stable Bohr orbit, the circumference must be an integral multiple of the de Broglie wavelength: $$2\pi r = n\lambda$$ Where $2\pi r$ = circumference, $n$ = principal quantum number (orbit number), $\lambda$ = de Broglie wavelength. --- **Step 2 - Substitution of Given Parameters** Given: * Orbit number: $n = 3$ (third orbit of $\ce{He^+}$) * Circumference: $2\pi r = x \text{ m}$ Substituting: $$x = 3\lambda$$ --- **Step 3 - Calculate de Broglie Wavelength** Solving for $\lambda$: $$\lambda = \frac{x}{3}$$ $$\lambda = \boxed{\frac{x}{3} \text{ m}}$$ --- **Step 4 - Explanation of Options** * **Option (A) is correct:** $\lambda = x/3$ m — direct result of the formula. * **Option (B) is incorrect:** $3x$ m would arise from multiplying instead of dividing. * **Option (C) is incorrect:** $x/9$ m would arise from incorrectly dividing by $n^2$. * **Option (D) is incorrect:** $9x$ m has no physical basis here.