Could someone help me with these questions. . . please
1. How does Rutherford’s model of the atom account for the back – scattering of alpha particles directed at the gold leaf
2. The higher the energy level occupied by an electron in the hydrogen atom, the larger the atom. The diameter of the atom is proportional to n2, where n=1 labels the lowest, or “ground” state, n=3 is the third state, and so on. If the atom’s diameter is 1x10-10m in its lowest energy state, what is its diameter in state number 50? How many unexcited atoms could be fit within this one giant atom
3. Briefly describe the Bohr model of the atom. What is Bohr’s key idea (involving matter waves) that makes the Bohr atom have discrete
energy levels?
I have answered these before. Please do some independent research to verify my answers. Google is a good start. Your text might be a good second place, although it it mentions Bohr's matter waves, I would toss the text without hesitation, as I stated before. It was DeBroglie who much later than Bohr postulated matter waves.
http://www.jiskha.com/display.cgi?id=1194307217
http://www.jiskha.com/display.cgi?id=1194362949
http://www.jiskha.com/display.cgi?id=1194698716
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Sure, I'll be happy to help you with these questions. Let's break them down one by one:
1. Rutherford’s model of the atom refers to the experiment conducted by Ernest Rutherford in which alpha particles were directed at a gold leaf. According to his model, atoms are mostly empty space with a small, dense, positively-charged nucleus at the center. However, since alpha particles are positively charged, they should have been repelled by the positively charged nucleus. Instead, Rutherford observed that some of the alpha particles were deflected backwards, which contradicted his original expectations.
To account for this back-scattering, Rutherford proposed that the positive charge of the atom is highly concentrated in its nucleus, while the mass of the atom is spread out in the surrounding empty space. This interpretation suggested that most of an atom's volume is empty, allowing the alpha particles to pass through, but some of them would come close enough to the nucleus to experience significant repulsion and be scattered back.
2. According to the given information, the diameter of the hydrogen atom in its lowest energy state (n=1) is 1x10^-10m. The diameter of the atom is proportional to n^2, where n is the energy level.
To find the diameter of the atom in state number 50, we can use the formula:
Diameter_n50 = Diameter_n1 * (n50^2 / n1^2)
Substituting the given values, we have:
Diameter_n50 = 1x10^-10m * (50^2 / 1^2)
Simplifying the expression, we get:
Diameter_n50 = 1x10^-10m * 2500
Diameter_n50 = 2.5x10^-7m
So, the diameter of the atom in state number 50 is 2.5x10^-7m.
To determine how many unexcited atoms could fit within this one giant atom, we need to compare the actual volumes of the atoms. The volume of a sphere is proportional to the cube of its diameter.
Volume_n50 = Volume_n1 * (Diameter_n50 / Diameter_n1)^3
Substituting the values, we get:
Volume_n50 = Volume_n1 * (2.5x10^-7m / 1x10^-10m)^3
Simplifying the expression, we have:
Volume_n50 = Volume_n1 * (2.5x10^3)^3
Volume_n50 = Volume_n1 * 15.625x10^9
Therefore, the number of unexcited atoms that could fit within this one giant atom is approximately 15.625x10^9.
3. The Bohr model of the atom, proposed by Niels Bohr, incorporates some principles from classical physics and introduces the idea of quantized energy levels. According to Bohr's model, electrons orbit the nucleus in specific energy levels or orbits, and each orbit corresponds to a different energy value.
Bohr's key idea involves matter waves. Bohr proposed that electrons possess wave-like characteristics and can only exist in certain stable orbits where their matter waves form complete standing waves. These stable orbits have quantized or discrete energy levels.
In other words, the electron can only exist in orbitals with energy levels corresponding to the standing wave patterns of its matter wave. These energy levels are distinct and separated by energy gaps, meaning the electron can transition between energy levels by emitting or absorbing discrete amounts of energy. This explains why atoms have discrete energy levels, rather than a continuous range of energies.