In this sentence, the section that modifies the subject—“unlike the modern model of the atom”—must proceed the main clause, rather than succeed it. "Unlike the modern model of the atom, the Bohr model states that electrons travel in fixed paths around the nucleus," fixes the problem.

In the sentence above, as it is written, it is not clear what the modifying phrase "After he returned from the long walk" is referring to. A chair cannot walk. In order to avoid a dangling modifier, a subject which can be appropriately modified by such a phrase must be included. The best way to change the underlined portion of the sentence above is: "the man settled into the chair on the porch."

The sentence above contains an example of a squinting modifier. It is not clear if the word "always" is meant to modify how often the young people listen to their elders, or how often they end up in trouble. This error must be corrected by changing the position of the modifier. The best way to correct the underlined portion of the sentence above is: "Young people who don't always listen to their elders wind up in trouble."

In the example sentence, it is not clear what the modifying phrase "Thrilled that the storm had finally broken" is referring to. Boots cannot be thrilled. In order to avoid a dangling modifier, a subject that can be appropriately modified by such a phrase must be included. The best way to change the underlined portion of the sentence above is: "the campers marched gleefully along the trail."

The sentence above contains an example of a squinting modifier. It is not clear if the word "vigilantly" is meant to modify how the old folks keep track of their health, or how they die from simple health complications. This error must be corrected by changing the position of the modifier. The best way to correct the underlined portion of the sentence above is: "Elderly people who don't vigilantly keep track of their health die from simple health complications."

The sentence is written with a dangling modifier, which makes the sentence read as though the "gruesome scene" was what was "coming back to the farm." The sentence needs to be restructured to clarify this problem. The only answer choice that does this is "everyone in the car saw the gruesome scene."

When a sentence begins with a dangling participle or descriptive phrase, the person or thing described in that phrase (in this case, "Neil") must immediately follow it. Only one answer choice does this correctly. The answer choice that begins "Neil's anxiety" may appear to do so, but it does not, because the possessive "Neil's" is no longer the subject, but is describing the anxiety.

The sentence as written contains a dangling modifier, as the construction of the sentence implies the skyscrapers are what is "coming around the corner." The word order can be changed to make this much more clear. The correct answer is "Coming around the corner, the people got a view of the skyscrapers across the river." 

The sentence as written contains a dangling modifier, in that "the sun" is not what is "coming upon the hills." The sentence needs to be rewritten to show that the travelers were the ones "coming upon the hills." "As the travelers came upon the hill, the sun began setting behind them," is the correct answer choice.

The best answer fixes the dangling participle that starts the sentence (the subject of the main clause should be the one doing the action described in the opening phrase), and uses a logical coordinator.