A hydrogen-like atom of atomic number Z transits from n=4 to n=3. The photon emitted from this transition is incident on a metal surface of threshold wavelength λth = 310nm. If the maximum kinetic energy of the emitted electron is 1.95ev, find the value of Z.
Correct Answer: 3
Solution and Explanation
\(\Psi =\frac{hc}{\lambda_{th}}=\frac{1240}{310}=4eV\)
\(KE_{max}=h\upsilon-\Psi\)
\(1.95=h\upsilon-4\Rightarrow h\upsilon=5.95eV\)
The energy of the photon emitted due to electron transition: \(\Delta E=13.6eV\,Z^2(\frac{1}{n_1^{2}}-\frac{1}{n_2^{2}})\)
\(5.95\,eV=13.6\,eV(Z)^2(\frac{1}{3^2}-\frac{1}{4^2})\)
Z=3
The correct answer is 3.
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Concepts Used:
Atom Structure Models
The three atomic models are as follows:
Thomson model:
Thomson atomic model was proposed by William Thomson in the year 1900. This model explained the description of an inner structure of the atom theoretically. It was strongly supported by Sir Joseph Thomson, who had discovered the electron earlier.
Thomson assumed that an electron is two thousand times lighter than a proton and believed that an atom is made up of thousands of electrons. In this atomic structure model, he considered atoms surrounded by a cloud having positive as well as negative charges. The demonstration of the ionization of air by X-ray was also done by him together with Rutherford. They were the first to demonstrate it. Thomson’s model of an atom is similar to a plum pudding.
Rutherford’s Alpha Scattering Experiment:
Rutherford’s conducted an experiment by bombarding a thin sheet of gold with α-particles and then studied the trajectory of these particles after their interaction with the gold foil.
Bohr’s Model of an Atom:
Bohr model of the atom was proposed by Neil Bohr in 1915. It came into existence with the modification of Rutherford’s model of an atom. Rutherford’s model introduced the nuclear model of an atom, in which he explained that a nucleus (positively charged) is surrounded by negatively charged electrons.
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