Wave Optics — Physics STD 12 Science — Question

statement$-1$ : The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100\; \Omega$ to $150\; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5$ $\times 10^{-3} /{ }^{\circ} C$

statement$-2\;: R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=\left(R-R_{0}\right) < < R_{0}$

$(A)$ The ratio of the longest wavelength to the shortest wavelength in Balmer series is $9 / 5$

$(B)$ There is an overlap between the wavelength ranges of Balmer and Paschen series.

$(C)$ The wavelengths of Lyman series are given by $\left(1+\frac{1}{ m ^2}\right) \lambda_0$, where $\lambda_0$ is the shortest wavelength of Lyman series and $m$ is an integer

$(D)$ The wavelength ranges of Lyman and Balmer series do not overlap